15-09-2021 Answers

1. If a:b = 4:9 and when 4 is added to both the numbers, the new ratio becomes 21:46. What is the difference between a and b?

Answer: 100

Solution: Let the numbers be 4x,9x.

(4x+4):(9x+4) = 21:46, Solving x=20,

Difference between a and b = 9x-4x = 5x = 100


2. The speed of three cars are in the ratio 2:3:4. Find the ratio between the time taken by these cars to travel the same distance.

Answer: 6:4:3

Solution: Speed is inversely proportional to time taken.

Hence ratio of time taken by these cars = (1/2) : (1/3) : (1/4) = 6:4:3


3. A earns Rs.120 in 5 days and B Rs.90 in 3 days. Find the ratio of earnings of A to B.

Answer: 4:5

Solution: A earns  120/5 = Rs.24 per day.

B earns 90/3 = Rs.30 per day.

Ratio of earnings = 24:30 = 4:5


4. A man, a woman and a boy earn in the ratio of 5 : 4 : 3. If 10 men, 16 women and 25 boys earn Rs.378. How much does each earn?

Answer: Man = Rs. 10, Woman = Rs. 8, Boy = Rs. 6

Solution: Let the amount earned by a man, a woman, a boy be 5x,4x,3x.

10*5x + 16*4x + 25*3x = 378,

x = 378/189 = 2.

Hence a man earns Rs.10, a woman Rs.8 and a boy Rs.6


5. A teacher distributed “n” chocolates among her students in the ratio 1/2 : 1/3 : 1/4 : 1/5. If each student receives at least one chocolate, find the minimum value of n.

Answer: 77

Solution: LCM of denominators 2,3,4,5 is 60.

Hence minimum value of n is 60*1/2 + 60*1/3 + 60*1/4 + 60*1/5 = 30+20+15+12 = 77


6. Find three numbers which are in the ratio of 5 : 4 : 3 and such that the sum of the greatest and the least exceeds the middle by 24.

Answer: 30, 24 and 18

Solution: Let the numbers be 5x,4x,3x.

8x - 4x = 24, x=6.

The numbers are 30,24,18


7. If a:b = 2:5, the value of (2a+3b):(7a+5b) is

Answer: 19/39

Solution: Dividing (2a+3b)/(7a+5b) by b,

we get (2a/b + 3)/(7a/b + 5)

As it is given a/b = 2/5,

(2a/b + 3)/(7a/b + 5) = (4/5 + 3)/(14/5 + 5) = 19/5/39/5 = 19/39


8. A certain amount is divided between A and B in the ratio 2 : 5. If A's share is Rs. 1400, find the total amount.

Answer: Rs. 4900

Solution: Let total amount be x.

x * 2/(2+5) = 1400. x = 4900


9. Which of the following ratio is invalid for two whole numbers whose sum is 72?

Answer: 3:4

Solution: The sum of ratio must not divide 72 completely (that is remainder as zero).

Hence 3:4 is invalid.


10. The weight of 13 m long iron rod is 23.4 kgs. Find the weight of 6 m long rod.

Answer: 10.8 kg

Solution: Required weight = 6 * 23.4/13 = 10.8 kg


11. The sum of three numbers A,B,C is 98. If A:B=2/3 and B:C=5/8, then B is

Answer: 30

Solution: A:B:C = 2*5:3*5:3*8 = 10:15:24

So, 98 = 10x+15x+24x,

x = 2,

B=15x = 30


12. If A : B = 7 : 9 and B : C = 3 : 5, then find A : B : C.

Answer:7 : 9 : 15

Solution: A:B:C = 7*3 : 9*3 : 9*5 = 7:9:15


13. The LCM of two numbers is 210 and their ratio is 2:3. The sum of these numbers is

Answer: 175

Solution: Let the numbers be 2x,3x.

LCM = 2*3*x = 210, x=35.

Sum of these numbers = 5x = 5*35 = 175


14. The ratio of two numbers is 3 : 4 and their sum is 420. Find the greater of the two numbers.

Answer: 240

Solution: Let the numbers be 3x,4x.

3x+4x=420,

x= 420/7 = 60.

The two numbers are 180, 240 of which 240 is greater


15. Three positive numbers are in the ratio 3:4:5, the sum of whose squares is 800. Find the numbers.

Answer: 12, 16, 20

Solution: Let the numbers be 3x, 4x and 5x

Then, 9x^2 + 16x^2 + 25x^2 = 800

50x^2 = 800 = x^2 = 16

x = 4 or -4. As the numbers are positive, x=4.

So, the numbers are 12, 16 and 20


16. Which of the two ratios are equal?

Answer: 2 : 5 and 14 : 35

Solution: Ans: 2 : 5 and 14 : 35


17. Find two numbers which are in the ratio of 5 : 4 and their cubes have difference of 1647.

Answer: 15 and 12

Solution: Let the numbers be 5x,4x.

Given 125x^3 - 64x^3 = 1647,

x^3 = 1647/61 = 27, x=3.

The two numbers are 15,12


18. One year payment to the servant is Rs. 200 plus one shirt. The servant leaves after 9 months and receives Rs. 120 and a shirt. Find the price of the shirt.

Answer: Rs.120

Solution: Let the shirt price be x.

For 9 months, he must receive Rs.150 and 3/4 th of the price of shirt.

So 150 + 0.75x = 120 + x,

x=120


19. If 4A=5B and 3A=2C, the ratio of B:C is

Answer: 8:15

Solution: A = 5B/4 = 2C/3,

15B = 8C,

B/C = 8/15


20. The average annual salary of all employees in a company was 10000. But the average salary for males was 10200 and for the females was 9200. What was the ratio of males and females employed?

Answer: 4:1

Solution: Using rule of alligation, ratio of female:male = (10200 - 10000)/(10000 - 9200) = 1/4

So for male:female it is 4/1 or 4:1

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