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 using the cost per kg of each variety. Let the ratio be x:y. According to the given information, (15x + 20y)/(x + y) = 16.50. Solving this equation, we get 15x + 20y = 16.50x + 16.50y. Simplifying further, we get 0.50x = 3.50y. Dividing both sides by y, we get (0.50x)/y = 3.50. Rearranging this equation, we get x/y = 7/3, which can be written as 7:03. Therefore, the correct answer is 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 the new person replaces one of the 8 persons, the total weight of the group increases by 2.5 kg. This means that the weight of the new person must be 2.5 kg more than the person they replaced. Since the person they replaced weighed 65 kg, the weight of the new person must be 65 kg + 2.5 kg = 67.5 kg. However, none of the given options match this weight, so the correct answer is "None of these".
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 man's 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 by using the formula: speed of boat in still water = (speed downstream + speed upstream) / 2. In this case, the boat covers a distance of 16 km downstream in 2 hours, so the speed downstream is 16 km/2 hours = 8 km/h. Similarly, the boat covers the same distance upstream in 4 hours, so the speed upstream is 16 km/4 hours = 4 km/h. Therefore, the speed of the boat in still water is (8 km/h + 4 km/h) / 2 = 6 km/h.
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 in still water is 2 km/h. On the other hand, he is able to travel 1 km along the current in 10 minutes, which means his speed with the current is 6 km/h.
To find the time it will take to go 5 km in stationary water, we can calculate the average speed. The average speed is given by the formula: average speed = total distance / total time.
In this case, the total distance is 5 km and the boatman's speed in still water is 2 km/h. Therefore, the total time it will take to go 5 km in stationary water is 5 km / 2 km/h = 2.5 hours.
Since 1 hour is equal to 60 minutes, 0.5 hours is equal to 30 minutes. Therefore, the boatman will take 2 hours and 30 minutes, or 1 hour and 30 minutes, to go 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 a tank in 2 days, it means that each pump can empty 1/16th of the tank in one hour. Therefore, if we want to empty the tank in 1 day with 4 pumps, each pump will need to work for 1/16th of the tank in one hour. Since there are 4 pumps, they will need to work for a total of 4/16th or 1/4th of the tank in one hour. Since there are 24 hours in a day, each pump will need to work for 24/4 or 6 hours in a day. Hence, 4 pumps must work for 6 hours a day to empty the tank in 1 day.
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 number of revolutions made by the larger wheel can be found by using the concept of gear ratios. The ratio of the number of cogs on the smaller wheel to the number of cogs on the larger wheel is 6:14, which can be simplified to 3:7. This means that for every 3 revolutions of the smaller wheel, the larger wheel completes 7 revolutions. Since the smaller wheel has made 21 revolutions, the larger wheel would have made 7 * (21/3) = 7 * 7 = 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 work requires a total of 36 x 18 = 648 man-days. To find out how many days it will take for 27 men to complete the same work, we can divide the total man-days by the number of men. Therefore, 648 man-days divided by 27 men gives us 24 days. Hence, 27 men will complete the same 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 on the 4 and the hour hand is on the 4. The minute hand is at the 12, while the hour hand is a quarter of the way between the 4 and the 5. Since there are 12 numbers on a clock face and 360 degrees in a circle, each number represents 30 degrees. Therefore, a quarter of the distance between 4 and 5 is 7.5 degrees. The angle between the minute hand and the hour hand is the difference between their positions, which is 30 degrees (minute hand) minus 7.5 degrees (hour hand), resulting in 22.5 degrees. However, since the question asks for the angle between the hands, the answer is the smaller angle, which 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
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 5% compound interest calculated on a half-yearly basis. The customer deposits Rs. 1600 on 1st January and 1st July of a year. At the end of the year, the interest gained will be calculated twice, once for the deposit made on 1st January and once for the deposit made on 1st July.
For the deposit made on 1st January:
The interest for the first half-year (January to June) will be (5/100) * Rs. 1600 = Rs. 80.
The amount at the end of the first half-year will be Rs. 1600 + Rs. 80 = Rs. 1680.
The interest for the second half-year (July to December) will be (5/100) * Rs. 1680 = Rs. 84.
The total interest for the deposit made on 1st January will be Rs. 80 + Rs. 84 = Rs. 164.
For the deposit made on 1st July:
The interest for the first half-year (July to December) will be (5/100) * Rs. 1600 = Rs. 80.
The amount at the end of the first half-year will be Rs. 1600 + Rs. 80 = Rs. 1680.
The interest for the second half-year (January to June) will be (5/100) * Rs. 1680 = Rs. 84.
The total interest for the deposit made on 1st July will be Rs. 80 + Rs. 84 = Rs. 164.
Therefore, the total interest gained by the customer at the end of the year will be Rs. 164 + Rs. 164 = Rs. 328. However, since the question asks for the amount gained by way of interest, we subtract the initial deposits made by the customer, which is Rs. 1600 + Rs. 1600 = Rs. 320. Hence, the answer is Rs. 328 - Rs. 320 = Rs. 8.
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 for compound interest: 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. In this case, the principal amount is Rs. 1200, the final amount is Rs. 1348.32, the time is 2 years, and we need to find the rate of interest. Plugging in these values into the formula, we get 1348.32 = 1200(1 + r/100)^(2). Solving this equation, we find that r is approximately 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
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
The fruit seller sells 40% of his apples and still has 420 apples remaining. This means that the 420 apples left represent 60% of his original stock. To find the original number of apples, we can set up the equation 60% of x = 420, where x is the original number of apples. Solving this equation, we find that x = 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 the remaining 80% were valid votes. Since one candidate received 55% of the total valid votes, the other candidate must have received the remaining 45% of the valid votes.
To calculate the number of valid votes the other candidate received, we can multiply the total number of votes (7500) by the percentage of valid votes (80%) and then multiply that by the percentage of votes received by the other candidate (45%):
7500 * 0.80 * 0.45 = 2700
Therefore, the number of valid votes that the other candidate got was 2700.
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 price. Therefore, the amount he will have to pay after the rebate is Rs. 6650 * 0.94 = Rs. 6251.
Then, he will have to pay a sales tax of 10% on this amount. Therefore, the amount he will have to pay after the sales tax is Rs. 6251 * 1.1 = 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 vowels together, we can treat them as a single entity, which means we have 7 entities to arrange (the 5 consonants and the 2 groups of vowels). The number of ways to arrange these entities is 7!. However, within each group of vowels, there are repetitions, so we need to divide by the factorial of the number of repetitions for each group. In this case, the 'O' appears twice, so we divide by 2!. Therefore, the total number of arrangements is 7! / (2!) = 50400.
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 last digit must be either 5 or 0. Since none of the digits can be repeated, there are 2 options for the last digit. For the first digit, there are 5 options (2, 3, 6, 7, 9) since 0 cannot be the first digit. For the second digit, there are 4 options (the remaining digits). Therefore, the total number of 3-digit numbers that can be formed is 2 (options for the last digit) multiplied by 5 (options for the first digit) multiplied by 4 (options for the second digit), which equals 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
There are 7 men and 3 women in total. We need to select a group of 5 men and 2 women. The number of ways to select 5 men out of 7 is given by the combination formula C(7,5) = 7! / (5! * (7-5)!) = 7! / (5! * 2!) = (7 * 6 * 5!) / (5! * 2 * 1) = (7 * 6) / (2 * 1) = 21. Similarly, the number of ways to select 2 women out of 3 is C(3,2) = 3! / (2! * (3-2)!) = 3! / (2! * 1) = 3. Therefore, the total number of ways to form the group is 21 * 3 = 63.
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 born at 3-year intervals is 50 years. To find the age of the youngest child, we need to divide the total age by the number of children. 50 divided by 5 equals 10. Therefore, the age of the youngest child is 10 years.
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
Let's assume the son's present age is x. According to the given information, the man is 24 years older than his son, so his present age would be x + 24. In two years, the man's age will be x + 24 + 2 and the son's age will be x + 2. It is stated that in two years, the man's age will be twice the age of his son. So, we can write the equation (x + 24 + 2) = 2(x + 2). Solving this equation, we get x = 22. Therefore, the present age of his son 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. To find Sachin's age, we can set up the equation 7x = 9(x-7), where x represents the common multiplier. Simplifying the equation, we get 7x = 9x - 63. Solving for x, we find x = 31.5. Therefore, Sachin's age is 31.5 - 7 = 24.5 years.
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 question states that the age of the father 10 years ago was thrice the age of his son. This can be represented as (F - 10) = 3(S - 10), where F is the father's current age and S is the son's current age. It is also 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). Solving these two equations, we get F = 40 and S = 20. Therefore, the ratio of their present ages is 40:20, which simplifies to 2:1 or 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 all three given numbers and leave the same remainder in each case is the greatest common divisor (GCD) of the three numbers. To find the GCD, we can use the Euclidean algorithm. The GCD of 1305 and 4665 is 105, and the GCD of 105 and 6905 is 5. Therefore, N is 5. The sum of the digits in 5 is 5, which is the correct answer.
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 evenly. To find the G.C.D., we can start by finding the prime factorization of each number. The prime factorization of 1.08 is 2^2 * 3^3, the prime factorization of 0.36 is 2^2 * 3^2, and the prime factorization of 0.9 is 2^1 * 3^2. To find the G.C.D., we take the smallest exponent for each prime factor. In this case, the smallest exponent for 2 is 1 and the smallest exponent for 3 is 2. Therefore, the G.C.D. is 2^1 * 3^2, which is equal to 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. We need to find the remainder when 2497 is divided by 60, which is 17. To make the sum divisible by 5, 6, 4, and 3, we need to add the difference between 60 and 17, which is 43. Therefore, the least number to be added is 43.
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 630. When we double 630, we get 1260, which is divisible by all the given numbers. Therefore, the least number that when doubled is divisible by 12, 18, 21, and 30 is 630.
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
The greatest possible length that can be used to measure exactly the lengths 7 m, 3 m 85 cm, and 12 m 95 cm is 35 cm. This is because 35 cm is a common factor of all the given lengths. By dividing each length by 35 cm, we get 20, 11, and 34 respectively, which are whole numbers. Therefore, 35 cm is the greatest possible length that can be used to measure all the given lengths accurately.
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. So, to find the greatest number that satisfies the given conditions, we need to find the highest common factor (HCF) of the differences between the dividends and the remainders.
The difference between 1657 and 6 is 1651, and the difference between 2037 and 5 is 2032. The HCF of 1651 and 2032 is 127. Therefore, 127 is the greatest number that satisfies the given conditions.
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 the equation, we get 3x = 2x + 8 + 3. Solving for x, we find that x = 11. Therefore, the third integer is 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
Explanation
The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. Let's assume the two-digit number is 10x + y, where x is the tens digit and y is the units digit. According to the given information, x + y = 15 and x - y = 3. Solving these two equations simultaneously, we get x = 9 and y = 6. So, the two-digit number is 96. However, the given answer is "Cannot be determined" which contradicts the solution obtained. Therefore, the question may be incomplete or not readable.
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. According to the given information, when we increase x by 17, it becomes equal to 60 times the reciprocal of x. Mathematically, this can be represented as x + 17 = 60 * (1/x). Simplifying this equation, we get x^2 + 17x - 60 = 0. Solving this quadratic equation, we find that x = 3 or x = -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. From the given information, we can form two equations:
1) x + y = 25
2) x - y = 13
By solving these equations simultaneously, we can find the values of x and y. Adding equation 1 and equation 2, we get:
2x = 38
x = 19
Substituting the value of x in equation 1, we get:
19 + y = 25
y = 6
The product of x and y 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
To find the length of the bridge, we need to calculate the distance covered by the train in 30 seconds. We know that the train is 130 meters long and is traveling at a speed of 45 km/hr. To convert the speed from km/hr to m/s, we divide it by 3.6. Therefore, the speed of the train is 45/3.6 = 12.5 m/s. In 30 seconds, the train will cover a distance of 12.5 m/s * 30 s = 375 meters. Since the train crosses the bridge during this time, the length of the bridge is 375 meters - 130 meters = 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, which is 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. This distance is equal to 10 km/hr * (36 seconds / 3600 seconds) = 100 meters. Since the length of the slower train is equal to the length of the faster train, the length of each train is 100 meters / 2 = 50 meters. Therefore, 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 in opposite directions, the relative speed of the trains 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 (1 kmph = 1000 m / 3600 s). Therefore, the relative speed is 200 kmph / 3.6 = 55.56 m/s. The time taken to cross the other train is given as 9 seconds. Using the formula distance = speed Ã— time, we can find the distance traveled by the train as 55.56 m/s Ã— 9 s = 500.04 m. However, the length of the first train is given as 270 m, so the length of the other train must be 500.04 m - 270 m = 230 m. Therefore, the correct answer is 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 running at a speed of 60 kmph, which is equivalent to 60,000 meters per hour. The relative speed between the train and the man is the sum of their speeds, as they are moving in opposite directions. Therefore, the relative speed is 60,000 + 6,000 = 66,000 meters per hour. To find the time it takes for the train to pass the man, we divide the length of the train (110 meters) by the relative speed (66,000 meters per hour). This gives us the time in hours, so we need to convert it to seconds by multiplying by 3600. The calculation is (110 / 66,000) * 3600 = 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, which means the length of the train is covered in that time. In 25 seconds, the train covers the length of the platform (100 meters) plus its own length. Therefore, the train takes an additional 10 seconds to cover its own length. Since the train takes 10 seconds to cover its own length, and the total time to cover the platform and its own length is 25 seconds, the length of the train must be 10/25 times 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
When two trains are running in opposite directions, their relative speed is the sum of their individual speeds. In this case, let the speed of each train be x km/hr. Since they cross each other in 12 seconds, the total distance covered by both trains is equal to the sum of their lengths, which is 240 meters. Converting this distance to kilometers, we get 0.24 km. Therefore, the relative speed of the trains is 0.24 km/12 sec = 0.02 km/sec. To convert this to km/hr, we multiply by 3600 (the number of seconds in an hour), giving us a relative speed of 72 km/hr. Since the relative speed is the sum of the individual speeds, each train must be traveling at 36 km/hr.
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 the sum of its own length and the distance the person has walked in 8.4 seconds. Similarly, when the train overtakes the second person, it covers a distance equal to the sum of its own length and the distance the person has walked in 8.5 seconds. Since the train covers the same distance in both cases, the ratio of the distances covered by the two persons in their respective times is equal to the ratio of their speeds. By equating these ratios and solving the equations, we can find that the speed of the train is 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
If the cost price of 20 articles is equal to the selling price of x articles, it means that the selling price of each article is equal to the cost price of each article. Since the profit is 25%, it means that the selling price is 125% of the cost price. Therefore, x must be equal to 16 because the selling price of 16 articles will be equal to the cost price of 20 articles.
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 the cost price. If his sale was Rs. 392, we can calculate his cost price by dividing the sale amount by 1 plus the profit percentage (1 + 22.5%). So, the cost price would be 392 / 1.225 = Rs. 320. His profit would then be the sale amount minus the cost price, which is 392 - 320 = Rs. 72. Therefore, his profit is 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 set up the equation: 85% of X = Rs. 18,700. Solving for X, we get X = Rs. 18,700 / 0.85 = Rs. 22,000.
To gain 15%, the plot must be sold for 115% of the original price. Therefore, the selling price should be 115% of Rs. 22,000, which is Rs. 22,000 * 1.15 = Rs. 25,300. Hence, the correct answer is Rs. 25,300.
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 meters A runs, B runs 4 meters. Since A has a head start of 140 m, A only needs to run 360 m to finish the race (500 m - 140 m). In the same time, B would have run 480 m (4/3 * 360 m). Therefore, A wins by a difference of 480 m - 360 m = 120 m. However, since A already had a head start of 140 m, the actual winning difference is 120 m - 140 m = 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 B is 8 points better than C. Therefore, if B were to give C a certain number of points, it would be fair for B to give C 8 points less than what A gave B, which is 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 the third number is x, then the first number is 1.2x (20% more) and the second number is 1.5x (50% more). To find the ratio, we divide the second number by the first number, which gives us (1.5x)/(1.2x) = 1.25. Simplifying this ratio gives us 5/4, which is equivalent to the ratio 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
When the number of boys and girls increase by 20% and 10% respectively, the new ratio can be found by multiplying the original ratio by the respective increase percentages.
The original ratio is 7:8.
Increasing the number of boys by 20% results in 7 * 1.2 = 8.4 boys.
Increasing the number of girls by 10% results in 8 * 1.1 = 8.8 girls.
Rounding these numbers to the nearest whole number, we get 8 boys and 9 girls.
Therefore, the new ratio is 8:9, which simplifies to 21:22.