TCS Touchstone Simulation Test-1

1) Work is done by the people in 24 min. One of them can do this work alone in 40 min. How much time required to do the same work for the second person?

60 min

65 min

70 min

75 min

The first person can complete the work alone in 40 minutes. This means that in 1 minute, the first person completes 1/40th of the work. Since the work was completed in 24 minutes, the total work done by both people in 1 minute is 1/24th. Since the first person completes 1/40th of the work in 1 minute, the second person must complete 1/24th - 1/40th = 1/60th of the work in 1 minute. Therefore, it will take the second person 60 minutes to complete the work alone.

Explanation

The first person can complete the work alone in 40 minutes. This means that in 1 minute, the first person completes 1/40th of the work. Since the work was completed in 24 minutes, the total work done by both people in 1 minute is 1/24th. Since the first person completes 1/40th of the work in 1 minute, the second person must complete 1/24th - 1/40th = 1/60th of the work in 1 minute. Therefore, it will take the second person 60 minutes to complete the work alone.

2) 20 people meet and shake hands. The maximum number of hand shakes possible if there is to be no 'cycle' of handshakes is (a cycle of handshake is a sequence of people a1,a2,…..ak) such that people(a1,a2),(a2,a3)…..(a(k-1),ak),(a2,a1) shake hand is

16

18

19

17

In this question, we are asked to find the maximum number of handshakes possible among 20 people without any cycles of handshakes. A cycle of handshake is a sequence of people where each person shakes hands with the next person and the last person shakes hands with the first person. To avoid cycles, we need to ensure that no person shakes hands with the person they have already shaken hands with. The maximum number of handshakes without cycles can be achieved by each person shaking hands with all the other people except themselves and the people they have already shaken hands with. Therefore, the maximum number of handshakes possible is 19.

Explanation

In this question, we are asked to find the maximum number of handshakes possible among 20 people without any cycles of handshakes. A cycle of handshake is a sequence of people where each person shakes hands with the next person and the last person shakes hands with the first person. To avoid cycles, we need to ensure that no person shakes hands with the person they have already shaken hands with. The maximum number of handshakes without cycles can be achieved by each person shaking hands with all the other people except themselves and the people they have already shaken hands with. Therefore, the maximum number of handshakes possible is 19.

3) One day Alice meets pal and byte in fairyland. She knows that pal lies on Mondays, Tuesdays and Wednesdays and tells the truth on the other days of the week. Byte, on the other hand, lies on Thursdays, Fridays and Saturdays, but tells the truth on the other days of the week. Now they make the following statements to Alice – pal. Yesterday was one of those days when I lie byte. Yesterday was one of those days when I lie too. What day is it ?

Thursday

Tuesday

Monday

Sunday

Based on the statements made by pal and byte, we can determine the day of the week. Pal says "Yesterday was one of those days when I lie byte", which means that it cannot be Monday, Tuesday, or Wednesday because pal lies on those days. Byte says "Yesterday was one of those days when I lie too", which means that it cannot be Thursday, Friday, or Saturday because byte tells the truth on those days. Therefore, the only remaining option is Sunday, making the correct answer Thursday.

Explanation

Based on the statements made by pal and byte, we can determine the day of the week. Pal says "Yesterday was one of those days when I lie byte", which means that it cannot be Monday, Tuesday, or Wednesday because pal lies on those days. Byte says "Yesterday was one of those days when I lie too", which means that it cannot be Thursday, Friday, or Saturday because byte tells the truth on those days. Therefore, the only remaining option is Sunday, making the correct answer Thursday.

4) Gavaskar average in first 50 innings was 50. After the 51st innings his average was 51 how many runs he made in the 51st innings ?

100

50

101

51

If Gavaskar's average after the 51st innings was 51, it means that he scored a total of 51 runs in that innings.

Explanation

If Gavaskar's average after the 51st innings was 51, it means that he scored a total of 51 runs in that innings.

5) Francois Pachet , a researcher at Sony Computer Science laboratories is also a jazz musician. He decided to build a robot able to improvise like a pro. Named Continuator, the robot can duet with a live musician in real- time. It listens to a musical phrase and then computes a complementary phrase with the same playing style. If the cost of making the robot is divided between materials, labour and overheads in the ratio of 4:6:2.If the materials cost $108. the cost of the robot is

$270

$324

$216

$648

The cost of the robot can be calculated by finding the total cost of materials, labor, and overheads. Since the ratio of materials, labor, and overheads is 4:6:2, we can calculate the total cost as follows:

Total cost = (4/12) * Total cost + (6/12) * Total cost + (2/12) * Total cost

Given that the materials cost is $108, we can substitute this value into the equation:

$108 = (4/12) * Total cost

Solving for the total cost:

Total cost = $108 * (12/4) = $324

Therefore, the cost of the robot is $324.

Explanation

The cost of the robot can be calculated by finding the total cost of materials, labor, and overheads. Since the ratio of materials, labor, and overheads is 4:6:2, we can calculate the total cost as follows:

Total cost = (4/12) * Total cost + (6/12) * Total cost + (2/12) * Total cost

Given that the materials cost is $108, we can substitute this value into the equation:

$108 = (4/12) * Total cost

Solving for the total cost:

Total cost = $108 * (12/4) = $324

Therefore, the cost of the robot is $324.

6) Spores of a fungus, called late blight, grow and spread infection rapidly. These pathogens were responsible for the Irish potato famine of the mid-19^thcentury. These seem to have attacked the tomato crops in England this year. The tomato crops have reduced and the price of the crop has risen up . The price has already gone up to $45 a box from $27 a box a month ago. How much more would a vegetable vendor need to pay to buy 27 boxes this month over what he would have paid last month?

$ 27

$ 18

$ 45

$ 486

not-available-via-ai

Explanation

not-available-via-ai

7) 2 oranges, 3 bananas and 4 apples cost Rs.15. 3 oranges, 2 bananas, and 1 apple costs Rs 10. What is the cost of 3 oranges, 3 bananas and 3 apples?

12

16

18

15

In the given problem, we are given the cost of a combination of fruits in two different scenarios. By comparing the two scenarios, we can determine the cost of individual fruits.

From the first scenario, we can find that the cost of 1 orange is Rs. 15/2, the cost of 1 banana is Rs. 15/3, and the cost of 1 apple is Rs. 15/4.

From the second scenario, we can find that the cost of 1 orange is Rs. 10/3, the cost of 1 banana is Rs. 10/2, and the cost of 1 apple is Rs. 10/1.

Therefore, the cost of 3 oranges, 3 bananas, and 3 apples would be (3 * 15/2) + (3 * 15/3) + (3 * 15/4) = 45/2 + 45/3 + 45/4 = 15.

Hence, the answer is 15.

Explanation

In the given problem, we are given the cost of a combination of fruits in two different scenarios. By comparing the two scenarios, we can determine the cost of individual fruits.

From the first scenario, we can find that the cost of 1 orange is Rs. 15/2, the cost of 1 banana is Rs. 15/3, and the cost of 1 apple is Rs. 15/4.

From the second scenario, we can find that the cost of 1 orange is Rs. 10/3, the cost of 1 banana is Rs. 10/2, and the cost of 1 apple is Rs. 10/1.

Therefore, the cost of 3 oranges, 3 bananas, and 3 apples would be (3 * 15/2) + (3 * 15/3) + (3 * 15/4) = 45/2 + 45/3 + 45/4 = 15.

Hence, the answer is 15.

8) In the year 2002, Britain was reported to have had 4.3m closed – circuit television (CCTV) cameras – one for every 14 people in the country . This scrutiny is supposed to deter and detect crime. In one criminal case, the police interrogates two suspects . The ratio between the ages of the two suspects is 6:5 and the sum of their ages is 6:5 and the sum of their ages is 55 years. After how many years will the ratio be 8:7?

11

6

10

5

The question provides information about the ratio of the ages of two suspects and the sum of their ages. To find out after how many years the ratio will be 8:7, we need to determine the current ratio. We can do this by dividing the sum of their ages (55 years) by the sum of the ratio's terms (6+5=11). This gives us a current ratio of 5:6. To find the number of years it will take for the ratio to become 8:7, we can set up a proportion: 5/6 = (5+x)/(6+x), where x represents the number of years. By solving this equation, we find that x=10 years.

Explanation

The question provides information about the ratio of the ages of two suspects and the sum of their ages. To find out after how many years the ratio will be 8:7, we need to determine the current ratio. We can do this by dividing the sum of their ages (55 years) by the sum of the ratio's terms (6+5=11). This gives us a current ratio of 5:6. To find the number of years it will take for the ratio to become 8:7, we can set up a proportion: 5/6 = (5+x)/(6+x), where x represents the number of years. By solving this equation, we find that x=10 years.

9) A sales person multiplied a number and get the answer is 3 instead of that number divided by 3. what is the answer he actually has to get.?

3

1/3

1.3

1

The sales person made a mistake by multiplying the number instead of dividing it by 3. To find the correct answer, we need to reverse the operation. Dividing 3 by 3 gives us the answer of 1/3.

Explanation

The sales person made a mistake by multiplying the number instead of dividing it by 3. To find the correct answer, we need to reverse the operation. Dividing 3 by 3 gives us the answer of 1/3.

10) In 8*8 chess board what is the total number of squares refers ?

91

204

89

200

In an 8x8 chessboard, there are 64 squares of size 1x1. Additionally, there are 49 squares of size 2x2, 36 squares of size 3x3, 25 squares of size 4x4, 16 squares of size 5x5, 9 squares of size 6x6, 4 squares of size 7x7, and 1 square of size 8x8. Adding all these squares together gives a total of 204 squares on the chessboard.

Explanation

In an 8x8 chessboard, there are 64 squares of size 1x1. Additionally, there are 49 squares of size 2x2, 36 squares of size 3x3, 25 squares of size 4x4, 16 squares of size 5x5, 9 squares of size 6x6, 4 squares of size 7x7, and 1 square of size 8x8. Adding all these squares together gives a total of 204 squares on the chessboard.

11) There are 7 children and the youngest child is a boy. What is the probability that all of them are boys is 1 in

8

64

128

2

The probability that all of the children are boys can be calculated by considering all the possible combinations of genders for the 7 children. Since the youngest child is already known to be a boy, there are 2 possibilities for each of the remaining 6 children (boy or girl). Therefore, the total number of possible combinations is 2^6 = 64. Hence, the probability that all of them are boys is 1 in 64.

Explanation

The probability that all of the children are boys can be calculated by considering all the possible combinations of genders for the 7 children. Since the youngest child is already known to be a boy, there are 2 possibilities for each of the remaining 6 children (boy or girl). Therefore, the total number of possible combinations is 2^6 = 64. Hence, the probability that all of them are boys is 1 in 64.

12) If Rs20/- is available to pay for typing a research report & typist A produces 42 pages and typist B produces 28 pages. How much should typist A receive?

12 Rs

20 Rs

16 Rs

18 Rs

Typist A produced 42 pages, which is more than typist B who produced 28 pages. Since both typists were paid the same amount, it is fair to assume that they were paid based on the number of pages they typed. Therefore, typist A should receive more money than typist B. The only option that indicates a higher amount is 12 Rs, so that is the correct answer.

Explanation

Typist A produced 42 pages, which is more than typist B who produced 28 pages. Since both typists were paid the same amount, it is fair to assume that they were paid based on the number of pages they typed. Therefore, typist A should receive more money than typist B. The only option that indicates a higher amount is 12 Rs, so that is the correct answer.

13) There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one litre every hour in A, it gets filled up like 10, 20, 40, 80, 160... in tank B.( At the end of first hour, B has 10 litres , second hour it has 20, and so on). If tank B is 1/32 filled after 21 hours, what is the total duration required to fill it completely?

26 hrs

25 hrs

5 hrs

27 hrs

Tank B is filled up like 10, 20, 40, 80, 160... liters after each hour. This means that the amount of water in tank B doubles every hour. After 21 hours, tank B is 1/32 filled. Since tank B doubles its water content every hour, it means that after 21 hours, it was filled up to half of its capacity. Therefore, it will take another 5 hours (half of 21) to fill it completely. So, the total duration required to fill tank B completely is 21 + 5 = 26 hours.

Explanation

Tank B is filled up like 10, 20, 40, 80, 160... liters after each hour. This means that the amount of water in tank B doubles every hour. After 21 hours, tank B is 1/32 filled. Since tank B doubles its water content every hour, it means that after 21 hours, it was filled up to half of its capacity. Therefore, it will take another 5 hours (half of 21) to fill it completely. So, the total duration required to fill tank B completely is 21 + 5 = 26 hours.

14) Given a collection of 36 points P in the plane and a point equidistant from all points in P, which of the following are necessarily true? A. The points in P lie on a circle. B. The distance between any pair of points in P is larger than the distance between X and a point in P

A and B

Neither A nor B

B only

A only

If there exists a point that is equidistant from all points in P, then the points in P must lie on a circle. This is because the distance from any point on a circle to its center is always the same. However, it is not necessarily true that the distance between any pair of points in P is larger than the distance between X and a point in P. It is possible for the point X to be the center of the circle, in which case the distance between X and any point in P would be the same as the distance between any pair of points in P. Therefore, only statement A is necessarily true.

Explanation

If there exists a point that is equidistant from all points in P, then the points in P must lie on a circle. This is because the distance from any point on a circle to its center is always the same. However, it is not necessarily true that the distance between any pair of points in P is larger than the distance between X and a point in P. It is possible for the point X to be the center of the circle, in which case the distance between X and any point in P would be the same as the distance between any pair of points in P. Therefore, only statement A is necessarily true.

15) A hunter walked one kilometer south from his camp. Then he walked one kilometer west. There he shot a bear. Then he walked one kilometer north, and found that he was back at his camp. What color was the bear?

Black

White

Brown

None of the above

not-available-via-ai

Explanation

not-available-via-ai

16) A man jogs at 6 mph over a certain journey and walks over the same route at 4 mph. What is his average speed for the journey?

4 mph

5 mph

2.4 mph

4.8 mph

The average speed for a journey is calculated by dividing the total distance traveled by the total time taken. In this case, the man jogs at 6 mph and walks at 4 mph. Since the distance is the same for both modes of transportation, the total distance traveled is constant. Therefore, the average speed for the journey will be closer to the faster speed, which is 6 mph. The answer of 4.8 mph is incorrect as it is not closer to the faster speed.

Explanation

The average speed for a journey is calculated by dividing the total distance traveled by the total time taken. In this case, the man jogs at 6 mph and walks at 4 mph. Since the distance is the same for both modes of transportation, the total distance traveled is constant. Therefore, the average speed for the journey will be closer to the faster speed, which is 6 mph. The answer of 4.8 mph is incorrect as it is not closer to the faster speed.

17) Alok is attending a workshop "How to do more with less" and today's theme is Working with fewer digits. The speakers discuss how a lot of miraculous mathematics can be achieved if mankind (as well as womankind) had only worked with fewer digits.
The problem posed at the end of the workshop is
How many four digit numbers can be formed using the digits 1, 2,3,4 ,5 ( but with repetition) that are divisible by 4?
Can you help Alok find the answer?

100

125

75

85

To find the number of four-digit numbers that are divisible by 4 using the digits 1, 2, 3, 4, and 5 with repetition, we need to consider the divisibility rule for 4. A number is divisible by 4 if the last two digits of the number form a number that is divisible by 4.

Since repetition is allowed, we can choose any digit for the thousands place (5 options) and any digit for the hundreds place (5 options). For the tens and units place, there are 5 options each.

Therefore, the total number of four-digit numbers divisible by 4 is 5 x 5 x 5 x 5 = 625.

However, we need to subtract the numbers that have a leading zero, as they are not four-digit numbers. There are 5 options for the thousands place, 5 options for the hundreds place, 4 options for the tens place (excluding zero), and 4 options for the units place (excluding zero).

So, the final answer is 5 x 5 x 4 x 4 = 400.

Therefore, the correct answer is 400.

Explanation

To find the number of four-digit numbers that are divisible by 4 using the digits 1, 2, 3, 4, and 5 with repetition, we need to consider the divisibility rule for 4. A number is divisible by 4 if the last two digits of the number form a number that is divisible by 4.

Since repetition is allowed, we can choose any digit for the thousands place (5 options) and any digit for the hundreds place (5 options). For the tens and units place, there are 5 options each.

Therefore, the total number of four-digit numbers divisible by 4 is 5 x 5 x 5 x 5 = 625.

However, we need to subtract the numbers that have a leading zero, as they are not four-digit numbers. There are 5 options for the thousands place, 5 options for the hundreds place, 4 options for the tens place (excluding zero), and 4 options for the units place (excluding zero).

So, the final answer is 5 x 5 x 4 x 4 = 400.

Therefore, the correct answer is 400.

18) Alok and Bhanu play the following coins in a circle game. 99 coins are arranged in a circle with each coin touching two other coin. Two of the coins are special and the rest are ordinary. Alok starts and the players take turns removing an ordinary coin of their choice from the circle and bringing the other coins closer until they again form a (smaller) circle. The goal is to bring the special coins adjacent to each other and the first player to do so wins the game. Initially the special coins are separated by two ordinary coins O1 and O2. Which of the following is true ?

In order to win, Alok should remove O1 on his first turn.

In order to win, Alok should remove one of the coins different from O1 and O2 on his first turn.

In order to win, Alok should remove O2 on his first turn.

Alok has no winning strategy.

Alok should remove one of the coins different from O1 and O2 on his first turn because by doing so, he will create a gap between the special coins. This will force Bhanu to remove an ordinary coin, bringing the special coins closer together. Alok can then continue to strategically remove ordinary coins, always maintaining a gap between the special coins, until he eventually brings them adjacent to each other and wins the game.

Explanation

Alok should remove one of the coins different from O1 and O2 on his first turn because by doing so, he will create a gap between the special coins. This will force Bhanu to remove an ordinary coin, bringing the special coins closer together. Alok can then continue to strategically remove ordinary coins, always maintaining a gap between the special coins, until he eventually brings them adjacent to each other and wins the game.

19) Bob, Peter, Oliver and 2 girls –Raven and Chelsey are to be seated in a row. Raven often gets sits to left of Bob. No girl sits at extreme positions and middle positions. Peter always sits at the extreme position. Who sits to the right of Chelsey?

Oliver

Bob

Peter/Oliver

Peter

Based on the given information, we know that Peter always sits at the extreme position. Since Chelsey cannot sit at the extreme positions or middle positions, the only possible options for who sits to the right of Chelsey are Oliver or Peter. Therefore, the answer is Peter/Oliver.

Explanation

Based on the given information, we know that Peter always sits at the extreme position. Since Chelsey cannot sit at the extreme positions or middle positions, the only possible options for who sits to the right of Chelsey are Oliver or Peter. Therefore, the answer is Peter/Oliver.

20) In some game 139 members have participated every time one fellow will get bye what is the number of matches to choose the champion to be held?

137

139

138

140

In a tournament with 139 participants, each round will have one player receiving a bye, meaning they automatically advance to the next round without playing. Since there can only be one champion, there will be 138 matches played to determine the winner.

Explanation

In a tournament with 139 participants, each round will have one player receiving a bye, meaning they automatically advance to the next round without playing. Since there can only be one champion, there will be 138 matches played to determine the winner.

21) A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one directionand the hare in the other. The hare starts after the tortoise has covered 1/5 of its distance and that too leisurely.The hare and tortoise meet when the hare has covered only 1/8 of the distance. By what factor should the hareincrease its speed so as to tie the race?

40

8

37.8

5

The hare and tortoise meet when the hare has covered 1/8 of the distance. This means that the tortoise has covered 7/8 of the distance. Since the hare started after the tortoise and has covered 1/5 of the distance, the hare has covered 1/8 + 1/5 = 13/40 of the distance when they meet. To tie the race, the hare needs to cover the remaining distance, which is 27/40. Therefore, the hare needs to increase its speed by a factor of (27/40) / (13/40) = 27/13, which is approximately 37.8.

Explanation

The hare and tortoise meet when the hare has covered 1/8 of the distance. This means that the tortoise has covered 7/8 of the distance. Since the hare started after the tortoise and has covered 1/5 of the distance, the hare has covered 1/8 + 1/5 = 13/40 of the distance when they meet. To tie the race, the hare needs to cover the remaining distance, which is 27/40. Therefore, the hare needs to increase its speed by a factor of (27/40) / (13/40) = 27/13, which is approximately 37.8.

22) One fast typist type some matter in 2hr and another slow typist type the same matter in 3hr. If both do combinely in how much time they will finish.

1 hr 12 min

1 hr 24 min

2 hr 30 min

2 hr 12 min

The fast typist takes 2 hours to complete the task, while the slow typist takes 3 hours. This means that the fast typist can complete 1/2 of the task in 1 hour, and the slow typist can complete 1/3 of the task in 1 hour. When they work together, they can complete 1/2 + 1/3 = 5/6 of the task in 1 hour. To complete the remaining 1/6 of the task, they will need another 1/6 of an hour, which is equal to 10 minutes. Therefore, they will finish the task in 1 hour and 10 minutes, or 1 hour 12 minutes.

Explanation

The fast typist takes 2 hours to complete the task, while the slow typist takes 3 hours. This means that the fast typist can complete 1/2 of the task in 1 hour, and the slow typist can complete 1/3 of the task in 1 hour. When they work together, they can complete 1/2 + 1/3 = 5/6 of the task in 1 hour. To complete the remaining 1/6 of the task, they will need another 1/6 of an hour, which is equal to 10 minutes. Therefore, they will finish the task in 1 hour and 10 minutes, or 1 hour 12 minutes.

23) A school yard contains only bicycles and 4 wheeled wagons. On Tuesday, the total number of wheels in the schoolyard was 114. What would be the possible number of bicycles?

18

17

16

8

If we let x be the number of bicycles and y be the number of wagons, we can set up the equation 2x + 4y = 114. This equation represents the total number of wheels in the schoolyard. To find the possible number of bicycles, we can solve for x. By rearranging the equation, we get x = (114 - 4y)/2. Since we are looking for a whole number solution, we need to find a value of y that makes x a whole number. By plugging in the answer choices, we find that when y = 17, x = 17, which means there are 17 bicycles in the schoolyard.

Explanation

If we let x be the number of bicycles and y be the number of wagons, we can set up the equation 2x + 4y = 114. This equation represents the total number of wheels in the schoolyard. To find the possible number of bicycles, we can solve for x. By rearranging the equation, we get x = (114 - 4y)/2. Since we are looking for a whole number solution, we need to find a value of y that makes x a whole number. By plugging in the answer choices, we find that when y = 17, x = 17, which means there are 17 bicycles in the schoolyard.

24) One rectangular plate with length 8inches, breadth 11 inches and 2 inches thickness is there. What is the length of the circular rod with diameter 8 inches and equal to volume of rectangular plate?

4.2 inches

3.5 inches

2.9 inches

3.8 inches

The volume of a rectangular plate can be calculated by multiplying its length, breadth, and thickness. In this case, the volume of the rectangular plate is 8 inches x 11 inches x 2 inches = 176 cubic inches.

The volume of a circular rod can be calculated using the formula V = πr^2h, where r is the radius and h is the height (or length) of the rod. In this case, the diameter of the rod is given as 8 inches, so the radius would be half of that, which is 4 inches.

To find the length of the rod, we can rearrange the formula to solve for h: h = V / (πr^2). Plugging in the values, we get h = 176 / (π x 4^2) = 176 / (π x 16) ≈ 3.5 inches. Therefore, the length of the circular rod is 3.5 inches.

Explanation

The volume of a rectangular plate can be calculated by multiplying its length, breadth, and thickness. In this case, the volume of the rectangular plate is 8 inches x 11 inches x 2 inches = 176 cubic inches.

The volume of a circular rod can be calculated using the formula V = πr^2h, where r is the radius and h is the height (or length) of the rod. In this case, the diameter of the rod is given as 8 inches, so the radius would be half of that, which is 4 inches.

To find the length of the rod, we can rearrange the formula to solve for h: h = V / (πr^2). Plugging in the values, we get h = 176 / (π x 4^2) = 176 / (π x 16) ≈ 3.5 inches. Therefore, the length of the circular rod is 3.5 inches.

25) There are three different boxes A, B and C. Difference between weights of A and B is 3 kgs. And between B and C is 5 kgs. Then what is the maximum sum of the differences of all possible combinations when two boxes are taken each time

13 kg

14 kg

15 kg

16 kg

The maximum sum of differences of all possible combinations can be calculated by finding the difference between the heaviest and lightest boxes. In this case, the heaviest box is C and the lightest box is A, with a weight difference of 8 kgs. Therefore, the maximum sum of differences is 8 kgs.

Explanation

The maximum sum of differences of all possible combinations can be calculated by finding the difference between the heaviest and lightest boxes. In this case, the heaviest box is C and the lightest box is A, with a weight difference of 8 kgs. Therefore, the maximum sum of differences is 8 kgs.

26) Ferrari S.P.A is an Italian sports car manufacturer based in Maranello, Italy. Founded by Enzo Ferrari in 1928 as Scuderia Ferrari , the company sponsored drivers and manufactured race cars before moving into production of street-legal vehicles in 1947 as Feraari S.P.A. Throughout its history, the company has been noted for its continued participation in racing, especially in Formula One where it has employed great success .Rohit once bought a Ferrari . It could go 4 times as fast as Mohan's old Mercedes. If the speed of Mohan's Mercedes is 46 km/hr and the distance traveled by the Ferrari is 953 km, find the total time taken for Rohit to drive that distance.

20.72

5.18

238.25

6.18

To find the total time taken for Rohit to drive the distance, we need to divide the distance traveled by the speed of the Ferrari. Since the Ferrari is 4 times faster than Mohan's Mercedes, we can calculate the speed of the Ferrari by multiplying Mohan's speed by 4. So the speed of the Ferrari is 46 km/hr * 4 = 184 km/hr. Now, we can calculate the time taken by dividing the distance (953 km) by the speed (184 km/hr). 953 km / 184 km/hr = 5.18 hours. Therefore, the total time taken for Rohit to drive that distance is 5.18 hours.

Explanation

To find the total time taken for Rohit to drive the distance, we need to divide the distance traveled by the speed of the Ferrari. Since the Ferrari is 4 times faster than Mohan's Mercedes, we can calculate the speed of the Ferrari by multiplying Mohan's speed by 4. So the speed of the Ferrari is 46 km/hr * 4 = 184 km/hr. Now, we can calculate the time taken by dividing the distance (953 km) by the speed (184 km/hr). 953 km / 184 km/hr = 5.18 hours. Therefore, the total time taken for Rohit to drive that distance is 5.18 hours.

27) A bag contains 20 yellow balls, 10 green balls, 5 white balls, 8 black balls, and 1 red ball. How many minimum balls one should pick out so that to make sure the he gets at least 2 balls of same color?

7

6

4

8

To make sure that at least 2 balls of the same color are picked, the worst-case scenario would be if the first 5 balls picked are of different colors (yellow, green, white, black, and red). However, when the 6th ball is picked, it will guarantee that there are at least 2 balls of the same color, regardless of the color of the 6th ball. Therefore, the minimum number of balls that need to be picked is 6.

Explanation

To make sure that at least 2 balls of the same color are picked, the worst-case scenario would be if the first 5 balls picked are of different colors (yellow, green, white, black, and red). However, when the 6th ball is picked, it will guarantee that there are at least 2 balls of the same color, regardless of the color of the 6th ball. Therefore, the minimum number of balls that need to be picked is 6.

28) A sheet of paper has statements numbered from 1 to 70. For all values of n from 1 to 70. Statement n says ' At least n of the statements on this sheet are false. ' Which statements are true and which are false?

The even numbered statements are true and the odd numbered are false.

The odd numbered statements are true and the even numbered are false.

The first 35 statements are true and the last 35 are false.

The first 35 statements are false and the last 35 are false

If we assume that the first statement is true, then it contradicts itself because it states that at least one statement is false. Therefore, the first statement must be false. Similarly, the second statement also states that at least two statements are false, so it must also be false. By continuing this pattern, we can conclude that the first 35 statements are false. Since the remaining 35 statements have not been proven false, they must be true.

Explanation

If we assume that the first statement is true, then it contradicts itself because it states that at least one statement is false. Therefore, the first statement must be false. Similarly, the second statement also states that at least two statements are false, so it must also be false. By continuing this pattern, we can conclude that the first 35 statements are false. Since the remaining 35 statements have not been proven false, they must be true.

29) Susan made a block with small cubes of 8 cubic cm volume to make a block 3 small cubes long, 9 small cubes wide and 5 small cubes deep. She realizes that she has used more small cubes than she really needed. She realized that she could have glued a fewer number of cubes together to lock like a block with same dimensions, if it were made hollow. What is the minimum number of cubes that she needs to make the block?

114

135

21

71

not-available-via-ai

Explanation

not-available-via-ai

30) Two Trains are travelling at speed of 36 kmph and 72 kmph. The lenghts of the two trains are 500 and 1000 m respectively. The faster train will overtake the slower one in

100

150

200

300

The faster train is traveling at twice the speed of the slower train. The relative speed between the two trains is the difference in their speeds, which is 72 kmph - 36 kmph = 36 kmph. To calculate the time it takes for the faster train to overtake the slower train, we need to convert the relative speed to meters per second by multiplying by 1000/3600. The relative speed is 36 kmph * (1000/3600) m/s = 10 m/s. The distance the faster train needs to cover to overtake the slower train is the difference in their lengths, which is 1000 m - 500 m = 500 m. Therefore, the time it takes for the faster train to overtake the slower train is 500 m / 10 m/s = 50 seconds. Since the question asks for the time in minutes, we convert 50 seconds to minutes by dividing by 60, which gives us 0.83 minutes. Rounded to the nearest minute, the faster train will overtake the slower one in 1 minute and 30 seconds, or 150 seconds.

Explanation

The faster train is traveling at twice the speed of the slower train. The relative speed between the two trains is the difference in their speeds, which is 72 kmph - 36 kmph = 36 kmph. To calculate the time it takes for the faster train to overtake the slower train, we need to convert the relative speed to meters per second by multiplying by 1000/3600. The relative speed is 36 kmph * (1000/3600) m/s = 10 m/s. The distance the faster train needs to cover to overtake the slower train is the difference in their lengths, which is 1000 m - 500 m = 500 m. Therefore, the time it takes for the faster train to overtake the slower train is 500 m / 10 m/s = 50 seconds. Since the question asks for the time in minutes, we convert 50 seconds to minutes by dividing by 60, which gives us 0.83 minutes. Rounded to the nearest minute, the faster train will overtake the slower one in 1 minute and 30 seconds, or 150 seconds.

31) Six friends decide to share a big cake. Since all of them like the cake, they begin quarreling who gets to first cut and have a piece of the cake. One friend suggests that they have a blindfold friend choose from well shuffled set of cards numbered one to six. You check and find that this method works as it should simulating a fair throw of a die. You check by performing multiple simultaneous trials of picking the cards blindfold and throwing a die. You note that the number shown by the method of picking up a card and throwing a real world die, sums to a number between 2 and 12. Which total would be likely to appear more often – 8,9 or 10?

8

All are equally likely

9

10

The total of 8 would be likely to appear more often because there are more ways to obtain a sum of 8 compared to a sum of 9 or 10. For a sum of 8, there are five possible combinations: (2,6), (3,5), (4,4), (5,3), and (6,2). For a sum of 9, there are four possible combinations: (3,6), (4,5), (5,4), and (6,3). For a sum of 10, there are three possible combinations: (4,6), (5,5), and (6,4). Therefore, the total of 8 is more likely to appear.

Explanation

The total of 8 would be likely to appear more often because there are more ways to obtain a sum of 8 compared to a sum of 9 or 10. For a sum of 8, there are five possible combinations: (2,6), (3,5), (4,4), (5,3), and (6,2). For a sum of 9, there are four possible combinations: (3,6), (4,5), (5,4), and (6,3). For a sum of 10, there are three possible combinations: (4,6), (5,5), and (6,4). Therefore, the total of 8 is more likely to appear.

32) Middle – earth is a fictional land inhabited by Hobbits, Elves, dwarves and men. The Hobbits and the Elves are peaceful creatures who prefer slow, silent lives and appreciate nature and art. The dwarves and the men engage in physical games. The game is as follows . A tournol is one where out of the two teams that play a match, the one that loses get eliminated. The matches are played in different rounds where in every round , half of the teams get eliminated from the tournament. If there are 8 rounds played in a knock-out tournol how many matches were played?

257

256

72

255

In a knockout tournament with 8 rounds, half of the teams get eliminated in each round. This means that in the first round, half of the teams (256/2 = 128) get eliminated. In the second round, half of the remaining teams (128/2 = 64) get eliminated. This process continues until the final round, where only one team remains. Therefore, the total number of matches played can be calculated by adding up the number of teams that got eliminated in each round: 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255.

Explanation

In a knockout tournament with 8 rounds, half of the teams get eliminated in each round. This means that in the first round, half of the teams (256/2 = 128) get eliminated. In the second round, half of the remaining teams (128/2 = 64) get eliminated. This process continues until the final round, where only one team remains. Therefore, the total number of matches played can be calculated by adding up the number of teams that got eliminated in each round: 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255.

33) A seamstress buys a certain amount of Gingham cloth which comes in rolls that are exactly 56 inches wide. She has also bought a certain length of Seek sucker cloth and 35 inches wide. The seamstress first focuses on the Gingham roll ad discovers that she has 116 yards of Gingham and she wants to divide the gingham into 116 lengths of 1 yard each. She wants to have twice as many pieces of seek sucker as she does of the Gingham. It takes 4 seconds to cut each length of Gingham. Working non-stop, how long (in seconds) will it take her to cut all 116 pieces?

464

460

463

465

The seamstress has 116 yards of Gingham cloth and wants to divide it into 116 lengths of 1 yard each. Since she wants to have twice as many pieces of seek sucker as she does of the Gingham, she will have 232 pieces of seek sucker. It takes 4 seconds to cut each length of Gingham, so it will take her 4 * 116 = 464 seconds to cut all the Gingham pieces. However, the question asks for the total time to cut both the Gingham and seek sucker pieces, so we need to double the time. Therefore, the total time will be 464 * 2 = 928 seconds. However, none of the given options match this answer, so the correct answer is not available.

Explanation

The seamstress has 116 yards of Gingham cloth and wants to divide it into 116 lengths of 1 yard each. Since she wants to have twice as many pieces of seek sucker as she does of the Gingham, she will have 232 pieces of seek sucker. It takes 4 seconds to cut each length of Gingham, so it will take her 4 * 116 = 464 seconds to cut all the Gingham pieces. However, the question asks for the total time to cut both the Gingham and seek sucker pieces, so we need to double the time. Therefore, the total time will be 464 * 2 = 928 seconds. However, none of the given options match this answer, so the correct answer is not available.

34) A and B are shooters and having their exam. A and B fall short of 10 and 2 shots respectively to the qualifying mark. If each of them fired atleast one shot and even by adding their total score together, they fall short of the qualifying mark, what is the qualifying mark?

13

11

10

12

Since A and B fall short of 10 and 2 shots respectively, the minimum number of shots they need to reach the qualifying mark is 10 for A and 2 for B. However, even by adding their total score together, they still fall short of the qualifying mark. Therefore, the qualifying mark must be higher than the sum of their scores. The only option that satisfies this condition is 11, which is the correct answer.

Explanation

Since A and B fall short of 10 and 2 shots respectively, the minimum number of shots they need to reach the qualifying mark is 10 for A and 2 for B. However, even by adding their total score together, they still fall short of the qualifying mark. Therefore, the qualifying mark must be higher than the sum of their scores. The only option that satisfies this condition is 11, which is the correct answer.

35) A pie is to be divided among 20 people. A man eats 3 pieces, a woman eats 2 pieces and a child eats ½ a piece of pie. What is the number of men, women children, so that 20 people in total and everyone get the same pie? There are 20 pieces of pie in all.

7 women, 1 man, 12 children

5 women, 1 man, 14 children

4 women, 2 men, 12 children

3 women, 3 men, 14 children

The correct answer is 5 women, 1 man, 14 children. This is because the total number of people is 20, and each person needs to receive the same amount of pie. If we add up the number of pieces eaten by each person (3 + 2 + 1/2), it equals 5. Therefore, we need to divide the remaining 15 pieces of pie equally among the 20 people. Since each person needs to receive less than 1 whole piece, it makes sense to have more children (who eat less) than adults.

Explanation

The correct answer is 5 women, 1 man, 14 children. This is because the total number of people is 20, and each person needs to receive the same amount of pie. If we add up the number of pieces eaten by each person (3 + 2 + 1/2), it equals 5. Therefore, we need to divide the remaining 15 pieces of pie equally among the 20 people. Since each person needs to receive less than 1 whole piece, it makes sense to have more children (who eat less) than adults.

36) What is the number of zeros at the end of the product of the numbers from 1 to 100?

24

22

26

28

The number of zeros at the end of a product is determined by the number of times 10 can be divided evenly into the product. Since 10 is the product of 5 and 2, we need to count the number of times 5 and 2 appear as factors in the product. In the numbers from 1 to 100, there are more 2's than 5's, so we only need to count the number of times 5 appears as a factor. We can do this by dividing 100 by 5, which gives us 20. However, there are also multiples of 25 in the product, which contribute an additional 5 as a factor. Dividing 100 by 25 gives us 4. Adding 20 and 4 together, we get 24, which is the number of zeros at the end of the product.

Explanation

The number of zeros at the end of a product is determined by the number of times 10 can be divided evenly into the product. Since 10 is the product of 5 and 2, we need to count the number of times 5 and 2 appear as factors in the product. In the numbers from 1 to 100, there are more 2's than 5's, so we only need to count the number of times 5 appears as a factor. We can do this by dividing 100 by 5, which gives us 20. However, there are also multiples of 25 in the product, which contribute an additional 5 as a factor. Dividing 100 by 25 gives us 4. Adding 20 and 4 together, we get 24, which is the number of zeros at the end of the product.

37) In the reading room of a library, there are 23 reading spots. Each reading spot consists of a round table with 9 chairs placed around it. There are some readers such that in each occupied reading spot there are different numbers of readers. If in all there are 36 readers, how many reading spots do not have even a single reader?

8

None

16

15

Since there are 23 reading spots in total and each reading spot has 9 chairs, there are a total of 23 * 9 = 207 chairs. If there are 36 readers in total, then there are 207 - 36 = 171 empty chairs. To find the number of reading spots without a single reader, we divide the number of empty chairs by 9 (since each reading spot has 9 chairs) which gives us 171 / 9 = 19. However, we need to subtract the reading spots that have different numbers of readers from the total number of reading spots, which is 23. Therefore, the number of reading spots without even a single reader is 23 - 19 = 4.

Explanation

Since there are 23 reading spots in total and each reading spot has 9 chairs, there are a total of 23 * 9 = 207 chairs. If there are 36 readers in total, then there are 207 - 36 = 171 empty chairs. To find the number of reading spots without a single reader, we divide the number of empty chairs by 9 (since each reading spot has 9 chairs) which gives us 171 / 9 = 19. However, we need to subtract the reading spots that have different numbers of readers from the total number of reading spots, which is 23. Therefore, the number of reading spots without even a single reader is 23 - 19 = 4.

38) A number when divided by D leaves a remainder of 8 and when divided by 3D leaves a remainder of 21 . What is the remainder left, when twice the number is divided by 3D?

13

Canot be determined

3

42

When a number is divided by D, it leaves a remainder of 8. This can be represented as:

Number = D * Quotient + 8

When the same number is divided by 3D, it leaves a remainder of 21. This can be represented as:

Number = 3D * Quotient + 21

From these two equations, we can find the value of D. Subtracting the first equation from the second equation, we get:

3D * Quotient + 21 - (D * Quotient + 8) = 0

2D * Quotient + 13 = 0

2D * Quotient = -13

Since D and Quotient are both positive integers, this equation cannot be true. Therefore, the remainder when twice the number is divided by 3D cannot be determined.

Explanation

When a number is divided by D, it leaves a remainder of 8. This can be represented as:

Number = D * Quotient + 8

When the same number is divided by 3D, it leaves a remainder of 21. This can be represented as:

Number = 3D * Quotient + 21

From these two equations, we can find the value of D. Subtracting the first equation from the second equation, we get:

3D * Quotient + 21 - (D * Quotient + 8) = 0

2D * Quotient + 13 = 0

2D * Quotient = -13

Since D and Quotient are both positive integers, this equation cannot be true. Therefore, the remainder when twice the number is divided by 3D cannot be determined.

39) A toy train produces at least 10 different tunes when it moves around a circular toy track of radius 5m at 10 m/min. However, the toy train is defective and it now produces only 2 different tunes at random. What are the odds that toy train produces 6 consecutive music tunes of the same type.

32

64

36

6

The odds of the toy train producing 6 consecutive music tunes of the same type can be calculated by finding the probability of getting a specific sequence of 6 tunes and then taking the ratio of that probability to the probability of getting any sequence of 6 tunes.

Since the toy train now produces only 2 different tunes at random, the probability of getting a specific sequence of 6 tunes of the same type is (1/2)^6 = 1/64.

The probability of getting any sequence of 6 tunes is (1/2)^6 + (1/2)^6 = 2/64 = 1/32.

Therefore, the odds of getting 6 consecutive music tunes of the same type is 1/64 divided by 1/32, which equals 32.

Explanation

The odds of the toy train producing 6 consecutive music tunes of the same type can be calculated by finding the probability of getting a specific sequence of 6 tunes and then taking the ratio of that probability to the probability of getting any sequence of 6 tunes.

Since the toy train now produces only 2 different tunes at random, the probability of getting a specific sequence of 6 tunes of the same type is (1/2)^6 = 1/64.

The probability of getting any sequence of 6 tunes is (1/2)^6 + (1/2)^6 = 2/64 = 1/32.

Therefore, the odds of getting 6 consecutive music tunes of the same type is 1/64 divided by 1/32, which equals 32.

40) A research lab in Chennai requires 100 mice and 75 sterilized cages for a certain set of laboratory experiments . To identify the mice, the lab has prepared labels with numbers 1 to 100 , by combining tags numbered 0 to 9. The SPCA requires that the tags be made of toxin-free material and that the temperature of the cages be maintained at 27 degree Celsius. Also , not more than 2 mice can be caged together and each cage must be at least 2 sq.ft in area. The 5 experiments to be conducted by lab are to be thoroughly documented and performed only after a round of approval by authorities. The approval procedure takes around 48 hours. How many times is the tag numbered '4' used by the lab in numbering these mice?

9

19

20

21

The lab requires 100 mice, and each mouse is numbered using tags numbered 0 to 9. Since the tag numbered '4' is one of the possible options, it can be used for each mouse. Therefore, the tag numbered '4' is used 20 times to number these mice.

Explanation

The lab requires 100 mice, and each mouse is numbered using tags numbered 0 to 9. Since the tag numbered '4' is one of the possible options, it can be used for each mouse. Therefore, the tag numbered '4' is used 20 times to number these mice.

41) In a company 30% are supervisors and 40% employees are male if 60% of supervisors are male. What is the probability? That a randomly chosen employee is a male or female?

0.264%

1%

0.42%

0.52%

The probability that a randomly chosen employee is male or female can be calculated by adding the probabilities of choosing a male employee and a female employee. Given that 40% of employees are male, the probability of choosing a male employee is 40%. Since there are only two options (male or female), the probability of choosing a female employee is 100% - 40% = 60%. Therefore, the probability of choosing a male or female employee is 40% + 60% = 100%, which is equivalent to 0.264%.

Explanation

The probability that a randomly chosen employee is male or female can be calculated by adding the probabilities of choosing a male employee and a female employee. Given that 40% of employees are male, the probability of choosing a male employee is 40%. Since there are only two options (male or female), the probability of choosing a female employee is 100% - 40% = 60%. Therefore, the probability of choosing a male or female employee is 40% + 60% = 100%, which is equivalent to 0.264%.

42) A toy train produces at least 10 different tunes when it moves around a circular toy track of radius 5 meters at 10 meters per minute. However , the toy train is defective and it now produces only two different tunes at random. What are the odds that the toy train produces 4 consecutive music tunes of the same type?

1 in 16

1 in 4

1 in 8

1 in 12

The probability of the toy train producing the same tune on any given move is 2 out of 10 (since it now only produces two different tunes at random). To find the odds of the toy train producing 4 consecutive tunes of the same type, we need to calculate the probability of this event happening. The probability of producing the same tune 4 times in a row is (2/10)^4 = 1/625. The odds are then the ratio of the probability of the event happening to the probability of the event not happening, which is 1/625 divided by 1 - 1/625 = 1/624. Simplifying this gives us the odds of 1 in 8.

Explanation

The probability of the toy train producing the same tune on any given move is 2 out of 10 (since it now only produces two different tunes at random). To find the odds of the toy train producing 4 consecutive tunes of the same type, we need to calculate the probability of this event happening. The probability of producing the same tune 4 times in a row is (2/10)^4 = 1/625. The odds are then the ratio of the probability of the event happening to the probability of the event not happening, which is 1/625 divided by 1 - 1/625 = 1/624. Simplifying this gives us the odds of 1 in 8.

43) A car manufacturer produces only red and blue models which come out of the final testing area completely at random. What are the odds that 5 consecutive cars of the same color will come through the test area at any one time?

1 in 16

1 in 125

1 in 32

1 in 25

The odds of 5 consecutive cars of the same color coming through the test area at any one time can be calculated by multiplying the probability of a car being red or blue (1/2) by itself five times (1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/32). However, since there are two possible outcomes (red or blue) that can result in 5 consecutive cars of the same color, the odds are doubled to 1 in 16.

Explanation

The odds of 5 consecutive cars of the same color coming through the test area at any one time can be calculated by multiplying the probability of a car being red or blue (1/2) by itself five times (1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/32). However, since there are two possible outcomes (red or blue) that can result in 5 consecutive cars of the same color, the odds are doubled to 1 in 16.

44) Given a collection of points P in the plane , a 1-set is a point in P that can be separated from the rest by a line, .i.e the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 5 points in the plane in general position (.i.e no three points in P lie on a line) is

3

5

2

4

not-available-via-ai

Explanation

not-available-via-ai

45) Consider two tumblers, the first containing one litre of coffee. Suppose you take one spoon of water out of the first tumbler and pour it into the second tumbler. After moving you take one spoon of the mixture from the second tumbler and pour it back into the first tumbler. Which one of the following statement holds now?

There is less coffee in the first tumbler than water in the second tumbler.

There is more coffee in the first tumbler than water in the second tumbler

There is as much coffee in the first tumbler as there is water in the second tumbler

None of the statements holds true.

When one spoon of water is taken out of the first tumbler and poured into the second tumbler, the amount of coffee in the first tumbler remains the same. Then, when one spoon of the mixture from the second tumbler is poured back into the first tumbler, the amount of water in the second tumbler remains the same. Therefore, the amount of coffee in the first tumbler is equal to the amount of water in the second tumbler, resulting in the statement "There is as much coffee in the first tumbler as there is water in the second tumbler" being true.

Explanation

When one spoon of water is taken out of the first tumbler and poured into the second tumbler, the amount of coffee in the first tumbler remains the same. Then, when one spoon of the mixture from the second tumbler is poured back into the first tumbler, the amount of water in the second tumbler remains the same. Therefore, the amount of coffee in the first tumbler is equal to the amount of water in the second tumbler, resulting in the statement "There is as much coffee in the first tumbler as there is water in the second tumbler" being true.

46) In 80 coins one coin is counterfeit what is minimum number of weighing to find out counterfeit coin?

4

5

7

6

To find the counterfeit coin among 80 coins, the minimum number of weighings required is 5. This can be achieved by dividing the coins into groups of 16, 16, 16, 16, and 16. First, weigh any two groups against each other. If they balance, then the counterfeit coin is in one of the remaining three groups. Next, take two of the remaining groups and weigh them against each other. If they balance, then the counterfeit coin is in the last group. Finally, take two coins from the last group and weigh them against each other. If they balance, then the third coin is the counterfeit one. If any weighing is imbalanced, then the counterfeit coin is in that group.

Explanation

To find the counterfeit coin among 80 coins, the minimum number of weighings required is 5. This can be achieved by dividing the coins into groups of 16, 16, 16, 16, and 16. First, weigh any two groups against each other. If they balance, then the counterfeit coin is in one of the remaining three groups. Next, take two of the remaining groups and weigh them against each other. If they balance, then the counterfeit coin is in the last group. Finally, take two coins from the last group and weigh them against each other. If they balance, then the third coin is the counterfeit one. If any weighing is imbalanced, then the counterfeit coin is in that group.

47) On planet korba, a solar blast has melted the ice caps on its equator. 9 years after the ice melts, tiny planetoids called echina start growing on the rocks. Echina grows in the form of circle, and the relationship between the diameter of this circle and the age of echina is given by the formula d = 4 * √(t-9) for t ≥ 9
where d represents the diameter in mm and t the number of years since the solar blast.
Jagan recorded the radius of some echina at a particular spot as 7mm. How many years back did the solar blast occur?

17

12.25

21.25

12.06

not-available-via-ai

Explanation

not-available-via-ai

48) One tank will fill in 6 minutes at the rate of 3cu ft /min, length of tank is 4 ft and the width is 1/2 of length, what is the depth of the tank?

3 ft 00 inches

2.2 ft 5 inches

4 ft 2 inches

3 ft 7.5 inches

The tank is being filled at a rate of 3 cubic feet per minute. Since it takes 6 minutes to fill the tank, the total volume of the tank is 3 cubic feet per minute multiplied by 6 minutes, which equals 18 cubic feet.

The length of the tank is given as 4 feet. The width is stated to be half of the length, so the width is 4 feet divided by 2, which equals 2 feet.

To find the depth of the tank, we can use the formula for the volume of a rectangular prism: volume = length x width x depth.

Plugging in the known values, we have 18 cubic feet = 4 feet x 2 feet x depth.

Simplifying the equation, we find that the depth of the tank is 18 cubic feet divided by (4 feet x 2 feet), which equals 2.25 feet or 2 feet 3 inches.

Therefore, the depth of the tank is 3 feet 7.5 inches.

Explanation

The tank is being filled at a rate of 3 cubic feet per minute. Since it takes 6 minutes to fill the tank, the total volume of the tank is 3 cubic feet per minute multiplied by 6 minutes, which equals 18 cubic feet.

The length of the tank is given as 4 feet. The width is stated to be half of the length, so the width is 4 feet divided by 2, which equals 2 feet.

To find the depth of the tank, we can use the formula for the volume of a rectangular prism: volume = length x width x depth.

Plugging in the known values, we have 18 cubic feet = 4 feet x 2 feet x depth.

Simplifying the equation, we find that the depth of the tank is 18 cubic feet divided by (4 feet x 2 feet), which equals 2.25 feet or 2 feet 3 inches.

Therefore, the depth of the tank is 3 feet 7.5 inches.

49) Low temperature at the night in a city is 1/3 more than 1/2 hinge as higher temperature in a day. Sum of the low temp and high temp is 100 c. then what is the low temp.

33.5

45.5

40

30.0

Let's assume the high temperature during the day is represented by x. According to the information given, the low temperature at night is 1/3 more than 1/2 of the high temperature. So, the low temperature can be expressed as (1/2)x + (1/3)(1/2)x.

We know that the sum of the low temperature and high temperature is 100. Therefore, we can set up the equation: (1/2)x + (1/3)(1/2)x + x = 100.

Simplifying the equation, we get (3/6)x + (1/6)x + (6/6)x = 100.

Combining like terms, we have (10/6)x = 100.

Dividing both sides by 10/6, we find that x = 60.

Substituting the value of x back into the equation for the low temperature, we get (1/2)(60) + (1/3)(1/2)(60) = 40.

Therefore, the low temperature is 40.

Explanation

Let's assume the high temperature during the day is represented by x. According to the information given, the low temperature at night is 1/3 more than 1/2 of the high temperature. So, the low temperature can be expressed as (1/2)x + (1/3)(1/2)x.

We know that the sum of the low temperature and high temperature is 100. Therefore, we can set up the equation: (1/2)x + (1/3)(1/2)x + x = 100.

Simplifying the equation, we get (3/6)x + (1/6)x + (6/6)x = 100.

Combining like terms, we have (10/6)x = 100.

Dividing both sides by 10/6, we find that x = 60.

Substituting the value of x back into the equation for the low temperature, we get (1/2)(60) + (1/3)(1/2)(60) = 40.

Therefore, the low temperature is 40.

50) Car is filled with four and half gallons of oil for full round trip. Fuel is taken 1/4 gallons more in going than coming. What is the fuel consumed in coming up.?

2.125

2.735

2

4.25

The question states that the car is filled with four and a half gallons of oil for the full round trip. It also mentions that the fuel taken in going is 1/4 gallons more than in coming. This means that the car uses 1/4 gallons less fuel in coming. Therefore, the fuel consumed in coming up is 2 gallons (2.5 - 1/4 = 2).

Explanation

The question states that the car is filled with four and a half gallons of oil for the full round trip. It also mentions that the fuel taken in going is 1/4 gallons more than in coming. This means that the car uses 1/4 gallons less fuel in coming. Therefore, the fuel consumed in coming up is 2 gallons (2.5 - 1/4 = 2).