1.
Sometimes we went off the road and on a path through the pine forest. The floor of the forest was soft to walk on; the frost did not happen it as it did the road. But we did not mind the hardness of the road because we had nails in the soles and heels nails bit on the frozen ruts and with nailed boots it was good walking on the road and invigorating. It was lovely walking in the woods.
2.
Write a paragraph on the summary of the story of " Your Favourite Movie "
3.
In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?
Correct Answer
C. 7:03
Explanation
The correct answer is 7:03. To find the ratio in which the two varieties of pulses should be mixed, we can set up a proportion based on their respective costs. Let the ratio be x:y. According to the given information, the cost of the first variety is Rs. 15 per kg and the cost of the second variety is Rs. 20 per kg. The average cost of the mixture is Rs. 16.50 per kg. Setting up the proportion, we get 15x + 20y = 16.50(x + y). Solving this equation, we find that x:y is equal to 7:03.
4.
The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
Correct Answer
C. 85 KG
Explanation
When a new person weighing 65 kg replaces one of the 8 persons, the average weight of the group increases by 2.5 kg. This means that the total weight of the group increases by 2.5 kg multiplied by 8, which is 20 kg. Therefore, the weight of the new person must be 65 kg + 20 kg = 85 kg.
5.
A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:
Correct Answer
C. 10 kmph
Explanation
The man's speed with the current is 15 km/hr, and the speed of the current is 2.5 km/hr. To find the man's speed against the current, we subtract the speed of the current from the speed with the current. Therefore, the man's speed against the current is 15 km/hr - 2.5 km/hr = 12.5 km/hr.
6.
A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water?
Correct Answer
B. 6 KMPH
Explanation
The speed of the boat in still water can be calculated using the formula: Speed of boat in still water = (speed downstream + speed upstream)/2.
Given that the boat covers a distance of 16 km downstream in 2 hours, the speed downstream can be calculated as 16 km/2 hours = 8 kmph.
Similarly, the boat covers the same distance upstream in 4 hours, so the speed upstream can be calculated as 16 km/4 hours = 4 kmph.
Using the formula, the speed of the boat in still water is (8 kmph + 4 kmph)/2 = 6 kmph.
Therefore, the correct answer is 6 kmph.
7.
A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?
Correct Answer
C. 1 HR 15 MIN
Explanation
The boatman is able to travel 2 km against the current in 1 hour, which means his speed against the current is 2 km/h. Similarly, he is able to travel 1 km along the current in 10 minutes, which means his speed along the current is 6 km/h. In stationary water, the boatman's speed will be the average of his speed against and along the current, which is (2+6)/2 = 4 km/h. Therefore, it will take him 5 km / 4 km/h = 1 hour and 15 minutes to travel 5 km in stationary water.
8.
3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?
Correct Answer
D. 12
Explanation
If 3 pumps working 8 hours a day can empty the tank in 2 days, it means that each pump can empty 1/3 of the tank in 2 days. Therefore, each pump can empty 1/6 of the tank in 1 day. To empty the tank in 1 day, we need 4 pumps working. Since each pump can empty 1/6 of the tank in 1 day, 4 pumps can empty 4/6 or 2/3 of the tank in 1 day. This means that 4 pumps need to work for 2/3 of a day or 16 hours. However, since we are looking for the number of hours a day, we round this up to the nearest whole number, which is 12 hours.
9.
A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
Correct Answer
B. 9
Explanation
The smaller wheel has 6 cogs and the larger wheel has 14 cogs. This means that for every revolution of the smaller wheel, the larger wheel will make 14/6 revolutions. So, when the smaller wheel has made 21 revolutions, the larger wheel will make 21 * (14/6) = 49 revolutions. Therefore, the correct answer is 49.
10.
36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?
Correct Answer
D. 24
Explanation
If 36 men can complete a piece of work in 18 days, it means that the total work requires 36 men x 18 days = 648 man-days. To find out how many days 27 men will take to complete the same work, we divide the total man-days by the number of men: 648 man-days / 27 men = 24 days. Therefore, 27 men will complete the work in 24 days.
11.
The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:
Correct Answer
B. 10 Degrees
Explanation
At 4:20, the minute hand is at the 4 on the clock, while the hour hand is slightly past the 4. The hour hand moves 30 degrees per hour, so at 4:20, it has moved 20/60 * 30 = 10 degrees. Therefore, the angle between the minute hand and the hour hand is 10 degrees.
12.
How many times in a day, are the hands of a clock in straight line but opposite in direction?
Correct Answer
B. 22
Explanation
The hour and minute hands of a clock are in a straight line but opposite in direction 11 times in a 12-hour period. Since there are 24 hours in a day, the hands of a clock will be in a straight line but opposite in direction 22 times in a day.
13.
A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:
Correct Answer
B. Rs 121
Explanation
The bank offers compound interest calculated on a half-yearly basis, which means that interest is added to the principal amount twice a year. The customer deposits Rs. 1600 on 1st January and 1st July, so there are two investment periods in a year.
For the first investment period (January to July), the customer gains interest on Rs. 1600 for 6 months at a rate of 5%. The interest gained in this period is (1600 * 5/100 * 6/12) = Rs. 40.
For the second investment period (July to December), the customer again gains interest on Rs. 1600 for 6 months at a rate of 5%. The interest gained in this period is also (1600 * 5/100 * 6/12) = Rs. 40.
Therefore, at the end of the year, the customer would have gained a total of Rs. 40 + Rs. 40 = Rs. 80 in interest. Adding this to the principal amount, the total amount gained is Rs. 1600 + Rs. 80 = Rs. 1680.
However, the question asks for the amount gained by way of interest only. Therefore, the correct answer is Rs. 80.
14.
At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?
Correct Answer
A. 6%
Explanation
To find the rate of compound interest, we can use the formula:
Amount = Principal * (1 + Rate/100)^Time
In this case, the principal is Rs. 1200, the amount is Rs. 1348.32, and the time is 2 years. Plugging in these values, we get:
1348.32 = 1200 * (1 + Rate/100)^2
Dividing both sides by 1200, we get:
1.1236 = (1 + Rate/100)^2
Taking the square root of both sides, we get:
1 + Rate/100 = 1.06
Subtracting 1 from both sides, we get:
Rate/100 = 0.06
Multiplying both sides by 100, we get:
Rate = 6%
Therefore, the correct answer is 6%.
15.
Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:
Correct Answer
C. Rs 1750
Explanation
The compound interest can be calculated using the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the rate of interest, n is the number of times interest is compounded per year, and t is the time in years.
Let's assume that the principal amount for the compound interest is x. Using the given information, we can set up the equation:
x(1 + 0.10/1)^(1*2) = 4000
Simplifying the equation, we get:
x(1.10)^2 = 4000
1.21x = 4000
x = 4000/1.21
x â‰ˆ 3305.79
Now, we can calculate the simple interest using the formula I = P * r * t:
I = P * 0.08 * 3
I = P * 0.24
Since the simple interest is half of the compound interest, we can set up the equation:
0.24P = 0.5 * 3305.79
0.24P = 1652.895
P â‰ˆ 1652.895/0.24
P â‰ˆ 6887.06
Therefore, the sum placed on simple interest is approximately Rs 6887.06. However, none of the given answer options match this value, so the correct answer cannot be determined.
16.
The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is:
Correct Answer
B. Rs 500
17.
A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:
Correct Answer
D. 700 apples
Explanation
If the fruit seller sells 40% of his apples and still has 420 apples, it means that 60% of the apples are equal to 420. To find the original number of apples, we can set up a proportion: 60/100 = 420/x. Cross-multiplying gives us 60x = 42000, and dividing both sides by 60 gives us x = 700. Therefore, the fruit seller originally had 700 apples.
18.
In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:
Correct Answer
A. 2700
Explanation
If 20% of the votes were invalid, then 100% - 20% = 80% of the votes were valid. Since one candidate got 55% of the valid votes, the other candidate must have received 80% - 55% = 25% of the valid votes.
To find the number of valid votes the other candidate got, we can calculate 25% of the total number of votes: 25% of 7500 = 0.25 * 7500 = 1875.
Therefore, the other candidate received 1875 valid votes. However, the answer options do not match this value. Therefore, the correct answer is not available.
19.
Rajeev buys good worth Rs. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods.
Correct Answer
A. Rs. 6876.10
Explanation
After getting a rebate of 6% on the goods worth Rs. 6650, Rajeev will have to pay 94% of the original cost, which is Rs. 6251. Rajeev then needs to pay a sales tax of 10% on this amount. The sales tax amount is calculated by multiplying Rs. 6251 by 10% (0.10), which equals Rs. 625.10. Therefore, the total amount Rajeev will have to pay for the goods is Rs. 6251 + Rs. 625.10 = Rs. 6876.10.
20.
In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
Correct Answer
D. 50400
Explanation
The word 'CORPORATION' has 11 letters, including 5 vowels (O, O, A, I, O). To arrange the letters such that the vowels always come together, we can treat the group of vowels (OOAIO) as one entity. This entity can be arranged in 5! = 120 ways. The remaining 6 letters (C, R, P, R, T, N) can be arranged in 6! = 720 ways. Therefore, the total number of arrangements is 120 * 720 = 86,400. However, since the two 'O' letters are repeated, we need to divide by 2! = 2 to account for the overcounting. Hence, the final answer is 86,400 / 2 = 43,200.
21.
How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?
Correct Answer
D. 20
Explanation
To form a 3-digit number that is divisible by 5, the units digit has to be either 5 or 0. Since none of the digits can be repeated, there are 2 choices for the units digit. For the hundreds digit, any of the remaining 4 digits can be chosen. And for the tens digit, any of the remaining 3 digits can be chosen. Therefore, the total number of 3-digit numbers that can be formed is 2 choices for the units digit multiplied by 4 choices for the hundreds digit multiplied by 3 choices for the tens digit, which equals 2 x 4 x 3 = 24. But since one of the choices for the hundreds digit is 0, which would make the number a 2-digit number, we have to subtract 4 from the total. Therefore, the correct answer is 20.
22.
In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
Correct Answer
A. 63
Explanation
The question asks for the number of ways to select a group of 5 men and 2 women from a total of 7 men and 3 women. To solve this, we can use the combination formula. The number of ways to select 5 men from 7 is 7C5 = 21, and the number of ways to select 2 women from 3 is 3C2 = 3. Multiplying these two results together gives us 21 * 3 = 63, which is the correct answer.
23.
The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
Correct Answer
A. 4
Explanation
The sum of the ages of the 5 children is 50 years. Since the ages are at intervals of 3 years each, we can assume that the ages are consecutive multiples of 3. Therefore, the ages could be 3, 6, 9, 12, and 15. However, the sum of these ages is 45, which is less than 50. Therefore, the ages must be 4, 7, 10, 13, and 16. The youngest child is 4 years old.
24.
A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
Correct Answer
D. 22 Years
Explanation
In this problem, let's assume the son's current age is x. According to the given information, the man is 24 years older than his son, so the man's current age would be x + 24. In two years, the man's age will be x + 24 + 2, and it will be twice the age of his son, which is 2(x + 2). Setting up this equation, we have x + 24 + 2 = 2(x + 2). Solving this equation, we find that x = 22, which represents the son's current age. Therefore, the correct answer is 22 years.
25.
Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?
Correct Answer
D. 24.5 Years
Explanation
Sachin is younger than Rahul by 7 years, and their ages are in the ratio of 7:9. This means that for every 7 years of Sachin's age, Rahul is 9 years old. To find Sachin's age, we can set up a proportion: 7/9 = 7+x/9+x, where x represents the additional years Sachin is older than Rahul. Cross-multiplying, we get 63+7x = 63+9x. Simplifying, we find that 2x = 0, which means x = 0. Therefore, Sachin is 7 years younger than Rahul, making him 24.5 years old.
26.
The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:
Correct Answer
B. 7 : 3
Explanation
The given information states that the father's age 10 years ago was thrice the age of his son. This can be represented as (F - 10) = 3(S - 10), where F represents the father's current age and S represents the son's current age. Similarly, it is given that ten years hence, the father's age will be twice that of his son. This can be represented as (F + 10) = 2(S + 10). By solving these two equations, we can find the ratio of their present ages, which is 7:3.
27.
Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:
Correct Answer
A. 4
Explanation
The greatest number that will divide 1305, 4665, and 6905, leaving the same remainder in each case is the greatest common divisor (GCD) of these three numbers. To find the GCD, we can use the Euclidean algorithm. Dividing 4665 by 1305 gives a quotient of 3 and a remainder of 750. Dividing 1305 by 750 gives a quotient of 1 and a remainder of 555. Finally, dividing 750 by 555 gives a quotient of 1 and a remainder of 195. Therefore, the GCD of 1305, 4665, and 6905 is 195. The sum of the digits in 195 is 1 + 9 + 5 = 15, which reduces to 1 + 5 = 6.
28.
The G.C.D. of 1.08, 0.36 and 0.9 is:
Correct Answer
C. 0.18
Explanation
The G.C.D. (Greatest Common Divisor) is the largest number that divides all the given numbers without leaving a remainder. To find the G.C.D., we need to factorize the given numbers. The factors of 1.08 are 1, 0.36, and 0.9 are 1, 2^2, and 3^2. The common factor among them is 1, which means the G.C.D. is 1.08. However, none of the answer choices is 1.08, so the correct answer must be the closest option to 1.08, which is 0.18.
29.
The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:
Correct Answer
C. 23
Explanation
To find the least number that should be added to 2497 so that the sum is divisible by 5, 6, 4, and 3, we need to find the least common multiple (LCM) of these numbers. The LCM of 5, 6, 4, and 3 is 60. To make the sum divisible by 60, we need to find the remainder when 2497 is divided by 60, which is 37. Therefore, we need to add 23 to 2497 to make the sum divisible by 5, 6, 4, and 3.
30.
What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30 ?
Correct Answer
B. 630
Explanation
To find the least number that is divisible by 12, 18, 21, and 30 when doubled, we need to find the least common multiple (LCM) of these numbers. The LCM of 12, 18, 21, and 30 is 1260. When this number is doubled, we get 2520. However, this is not the least number that satisfies the condition. The next multiple of 1260 is 3780, which is not necessary to consider. Therefore, the least number that when doubled is divisible by 12, 18, 21, and 30 is 1260.
31.
The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is:
Correct Answer
C. 35 cm
Explanation
To find the greatest possible length that can measure exactly 7 m, 3 m 85 cm, and 12 m 95 cm, we need to find the greatest common divisor (GCD) of these lengths.
First, we convert all the lengths to centimeters:
7 m = 700 cm
3 m 85 cm = 385 cm
12 m 95 cm = 1295 cm
Next, we find the GCD of these lengths, which is 35 cm. This means that a length of 35 cm can be used to measure all three lengths exactly. Therefore, the correct answer is 35 cm.
32.
The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:
Correct Answer
B. 127
Explanation
When a number is divided by another number, the remainder is always less than the divisor. In this case, the greatest number that leaves a remainder of 6 when divided by 1657 is 1657 - 6 = 1651. Similarly, the greatest number that leaves a remainder of 5 when divided by 2037 is 2037 - 5 = 2032. To find the greatest number that satisfies both conditions, we need to find the common factors of 1651 and 2032. The largest common factor is 127, which means that when 127 is divided by 1657 and 2037, it leaves remainders of 6 and 5 respectively. Therefore, the correct answer is 127.
33.
Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:
Correct Answer
D. 15
Explanation
Let's assume the first odd integer is x. The second odd integer would be x+2 and the third odd integer would be x+4. According to the given information, 3 times the first integer (3x) is equal to 3 more than twice the third integer (2(x+4)+3). Simplifying this equation, we get 3x = 2x + 8 + 3. Solving for x, we find that x = 11. Therefore, the third integer is x+4 = 11+4 = 15.
34.
The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?
Correct Answer
D. Cannot be determined
35.
Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number.
Correct Answer
A. 3
Explanation
Let's assume the positive number is x. The statement "when increased by 17" implies x + 17. The statement "equal to 60 times the reciprocal of the number" implies 60 * (1/x). According to the given information, we can write the equation as x + 17 = 60 * (1/x). By simplifying the equation, we get xÂ² + 17x - 60 = 0. Factoring the equation, we get (x - 3)(x + 20) = 0. Therefore, the possible values for x are 3 and -20. Since we are looking for a positive number, the correct answer is 3.
36.
The sum of two number is 25 and their difference is 13. Find their product.
Correct Answer
B. 114
Explanation
Let's assume the two numbers as x and y. We are given that their sum is 25 and their difference is 13. So, we can set up two equations: x + y = 25 and x - y = 13. Solving these equations simultaneously, we can find that x = 19 and y = 6. The product of these two numbers is 19 * 6 = 114.
37.
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
Correct Answer
C. 245 M
Explanation
The train is traveling at a speed of 45 km/hr, which is equivalent to 45000 meters per hour or 12.5 meters per second. In 30 seconds, the train will travel a distance of 30 * 12.5 = 375 meters. The train itself is 130 meters long. Therefore, the length of the bridge is the total distance traveled by the train (including the length of the train itself) minus the length of the train: 375 - 130 = 245 meters.
38.
Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:
Correct Answer
A. 50 M
Explanation
The faster train is overtaking the slower train, so the relative speed between the two trains is the difference between their speeds: 46 km/hr - 36 km/hr = 10 km/hr. In 36 seconds, the faster train covers a distance equal to its own length plus the length of the slower train. Let's assume the length of each train is L meters.
The distance covered by the faster train in 36 seconds is (10 km/hr * 36 seconds) / (3600 seconds/hr) = 100 meters.
Therefore, the length of each train is L = 100 meters / 2 = 50 meters.
Hence, the correct answer is 50 M.
39.
A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
Correct Answer
A. 230 M
Explanation
When two trains are moving towards each other, their relative speed is the sum of their individual speeds. In this case, the relative speed is 120 kmph + 80 kmph = 200 kmph. To convert this to meters per second, we divide by 3.6 (since 1 kmph = 1000 m/3600 s). Therefore, the relative speed is 200 kmph / 3.6 = 55.56 m/s. The length of the train being crossed is equal to the distance traveled by the first train in the time it takes to cross the other train. The distance traveled by the first train is equal to its speed multiplied by the time taken, which is 55.56 m/s * 9 s = 500 m. Therefore, the length of the other train is 500 m - 270 m (length of the first train) = 230 m.
40.
A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Correct Answer
B. 6 SEC
Explanation
The train is moving towards the man, so their relative speed is the sum of their speeds, which is (60 + 6) km/h = 66 km/h. To convert this speed to m/s, we divide by 3.6, so the relative speed is (66/3.6) m/s = 18.33 m/s. The train needs to cover a distance of 110 meters to pass the man, so the time taken is distance/speed = 110/18.33 = 6 seconds. Therefore, the train will pass the man in 6 seconds.
41.
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:
Correct Answer
B. 150 m
Explanation
The train takes 15 seconds to pass a stationary pole, indicating its own length. In 25 seconds, the train passes a platform that is 100 meters long, which includes both the length of the train and the extra distance it covers while passing the platform. Therefore, the length of the train is 100 meters longer than the length of the platform, which is 150 meters.
42.
Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
Correct Answer
C. 36
Explanation
The length of both trains combined is 240 meters (120 meters + 120 meters). They cross each other in 12 seconds, which means they cover a distance of 240 meters in 12 seconds. To find the speed, we need to convert the time and distance into the same units. 12 seconds is equal to 12/3600 hours (since 1 hour = 3600 seconds). Therefore, the speed of each train is (240 meters / 12/3600 hours) = 600 meters per hour. To convert this into kilometers per hour, we divide by 1000, giving us a speed of 0.6 kilometers per hour. Multiplying this by 60 to get the speed in kilometers per hour gives us 36 kilometers per hour.
43.
A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
Correct Answer
D. 81 KMPH
Explanation
When the train overtakes the first person, it covers a distance equal to its own length plus the distance the person has walked in 8.4 seconds. Similarly, when the train overtakes the second person, it covers a distance equal to its own length plus the distance the person has walked in 8.5 seconds.
Let's assume the length of the train is 'x' km.
For the first person, the distance covered by the train is x + (4.5 * (8.4/3600)) km.
For the second person, the distance covered by the train is x + (5.4 * (8.5/3600)) km.
Since the train takes the same amount of time to overtake both persons, we can equate the two distances.
x + (4.5 * (8.4/3600)) = x + (5.4 * (8.5/3600))
Simplifying the equation, we get:
(4.5 * (8.4/3600)) = (5.4 * (8.5/3600))
Solving for x, we find that x = 0.3 km.
Therefore, the length of the train is 0.3 km and the speed of the train is the distance covered in 8.4 seconds, which is (0.3 * 3600)/8.4 = 81 km/hr.
44.
The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:
Correct Answer
B. 16
Explanation
In this question, the cost price of 20 articles is equal to the selling price of x articles. This means that the selling price of each article is the same. Since the profit is 25%, the selling price is 125% of the cost price. Therefore, the value of x can be calculated by dividing 125% of the cost price of 20 articles by the selling price of each article. Simplifying this equation, we find that x is equal to 16.
45.
A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?
Correct Answer
C. Rs 72
Explanation
The shopkeeper expects a gain of 22.5% on his cost price. This means that he wants to make a profit of 22.5% of his cost price.
To find the cost price, we can use the formula:
Cost Price = Selling Price / (1 + Profit Percentage)
In this case, the selling price is Rs. 392 and the profit percentage is 22.5%.
Cost Price = 392 / (1 + 22.5/100) = 392 / 1.225 = Rs. 320
Now, to find the profit, we can subtract the cost price from the selling price:
Profit = Selling Price - Cost Price = 392 - 320 = Rs. 72
Therefore, the shopkeeper's profit was Rs. 72.
46.
When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?
Correct Answer
C. Rs 25300
Explanation
If the owner loses 15% when selling the plot for Rs. 18,700, it means that the selling price is only 85% of the original price. To find the original price, we can divide Rs. 18,700 by 0.85. This gives us Rs. 22,000.
To gain 15% profit, the selling price should be 115% of the original price. To find the selling price, we can multiply Rs. 22,000 by 1.15. This gives us Rs. 25,300.
Therefore, the plot must be sold for Rs. 25,300 in order to gain a 15% profit.
47.
In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by:
Correct Answer
C. 20 m
Explanation
In a 500 m race, the ratio of the speeds of A and B is 3:4. This means that for every 3 units of distance covered by A, B covers 4 units of distance. Since A has a head start of 140 m, A only needs to cover 360 m to finish the race (500 m - 140 m). Since A covers 3 units of distance for every 4 units covered by B, A's speed is 3/4 times that of B. Therefore, A will finish the race 3/4 times faster than B. So, A will win by 3/4 * 360 m = 270 m. However, A only wins by 20 m, so the correct answer is 20 m.
48.
In a game of 100 points, A can give B 20 points and C 28 points. Then, B can give C:
Correct Answer
B. 10 points
Explanation
If A can give B 20 points and C 28 points, it means that A is better than both B and C in the game. Therefore, B must be better than C. Since the difference between the points given by A to B and C is 8 (28-20), the difference between the points B can give to C must also be 8. Hence, B can give C 10 points.
49.
Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:
Correct Answer
C. 4 : 5
Explanation
If two numbers are respectively 20% and 50% more than a third number, it means that the first number is 20% greater than the third number and the second number is 50% greater than the third number. To find the ratio of the two numbers, we can express the first number as 100% + 20% = 120% of the third number, and the second number as 100% + 50% = 150% of the third number. Simplifying these percentages, we get the ratio of the two numbers as 120% : 150%. Dividing both sides by 10, we get the simplified ratio as 12 : 15, which further simplifies to 4 : 5.
50.
The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?
Correct Answer
C. 21:22
Explanation
The ratio of boys to girls in the college is initially 7:8. If the number of boys increases by 20%, then the new ratio of boys to girls would be (7 + 20% of 7) : 8 = 21:8. Similarly, if the number of girls increases by 10%, then the new ratio of boys to girls would be 21 : (8 + 10% of 8) = 21:22. Therefore, the new ratio is 21:22.