25-10-2021 Answers

 1. If 40% of a number is equal to two-third of another number, what is the ratio of the first number to the second number?

Answer: 5:3

Solution: Let the numbers be x,y.

40x/100 = 2y/3,

x/y = (2*100)/(3*40),

x/y = 5/3


2. Two numbers are in the ratio of 3 : 4. If 5 is subtracted from each, the resulting numbers are in the ratio 2 : 3. Find the numbers.

Answer: 15.20

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

3x-5:4x-5 = 2:3,

9x-15 = 8x-10,

x=5.

So the numbers are 15,20


3. If a=5b=2c=4d, then a:b:c:d is

Answer: 20:4:10:5

Solution: a/b = 5/1, b/c = 2/5, c/d = 2/1 (4/2 which is 2/1)

a:b:c:d = n1*n2*n3 : d1*n2*n3 : d1*d2*n3 : d1*d2*d3

= 5*2*2 : 1*2*2 : 1*5*2 : 1*5*1

= 20:4:10:5


4. The ratio of earnings of A to B is 4 : 7. What is the ratio of A's earning to the combined earning?

Answer: 4:11

Solution: Let the earnings be 4x,7x.

Required ratio = 4x/(4x+7x) = 4/11


5. The weights of Raju and Shyam is in the ratio 5 : 7. If the difference between their weights is 12 kgs, find Shyam's weight.

Answer: 42 kgs

Solution: Let the weights be 5x,7x.

7x-5x = 12,

x = 6 kgs.

Shyam's weight = 7x = 42 kgs


6. What is the ratio between numbers of vowels to that of consonants in English Alphabet?

Answer: 5:21

Solution: There are 5 vowels and 21 consonants. Hence the ratio is 5:21


7. Rs. 2600 is to be divided into three parts in the ratio of 6 : 4 : 3. Find each part.

Answer: 1200, 800, 600

Solution: Let the parts be 6x,4x,3x.

6x+4x+3x=2600,

x=200

The parts are 1200,800,600


8. Find the number which when added to 2, 14, 37 and 133 make them proportionate to each other.

Answer: 3

Solution: Let the number to be added be x.

(2+x)/(14+x) = (37+x)/(133+x),

266+133x+2x+x^2 = 37*14 + 14x + 37x + x^2,

135x-51x = 252, x = 3


9. Two whole numbers whose sum is 64 cannot be in the ratio

Answer: 1:2

Solution: 64 = 2*2*2*2*2*2

Hence the sum of ratio's must add upto power of 2.

(For example 48 and 16 it is 3:1 where 3+1 =4)

Hence the ratio 1:2 does not add up to a power of 2.


10. The ratio of heights of A and B is 5 : 7. If B's height is 175 cms, find A's height

Answer: 125 cms

Solution: A:B = 5:7, A = 5B/7,

As it is given B=175,

A = 5*175/7 = 5*25 = 125 cms


11. Five numbers m,n,o,p,q are in the ratio 2:3:5:8:9 and their sum is 162. Find the average of the four numbers m,n,o,p.

Answer: 27

Solution: Let the common factor be x.

162 = 2x+3x+5x+8x+9x, x=6

Average of m,n,o,p = 18x/4 = 18*6/4 = 27


12. The monthly salaries of A, B and C in the proportion of 2 : 3 : 5. If C's monthly salary is Rs. 1200 more than that of A, then find B's annual salary.

Answer: Rs. 14400

Solution: Let the salaries be 2x,3x,5x.

Given 5x-2x = 1200,

Solving x=400.

Hence B's monthly salary = 3x = 3*400 = 1200.

Annual salary = 1200*12 = 14400


13. The sides of a triangle are in the ratio 1/2 : 1/3 : 1/4 and its perimeter is 104 cm. The length of the longest side is

Answer: 48 cm

Solution: Let the sides be x/2,x/3,x/4.

Sum = x/2 + x/3 + x/4 = 104,

13x/12 = 104, x=96.

Longest side = x/2 = 96/2 = 48 cm


14. The side of a square and the radius of a circle are equal. Find the ratio of their area.

Answer: 7:22

Solution: Area of square = a^2

Area of circle = 22/7 * a^2

Hence ratio = 1:22/7 = 7:22


15. Find the mean proportional of 4 and 16.

Answer: 8

Solution: Let the mean proportional be x.

4/x = x/16,

x^2 = 64, Solving x=8 or -8.

Among the given options 8 is the answer.


16. What is the ratio between an hour and a second?

Answer: 3600 : 1

Solution: An hour = 60 minutes = 3600 seconds.

Hence ratio between an hour and a second = 3600:1


17. Two numbers are in the ratio 3 : 5. If each number is increased by 10, the ratio becomes 5 : 7. Find the numbers

Answer: 15 and 25

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

(3x+10)/(5x+10) = 5/7,

21x+70 = 25x+50, x=5.

Hence the numbers are 15,25.


18. A's salary is Rs. 500 per month and that of B's is Rs. 9000 per annum. Find the ratio of A's salary to that of B's.

Answer: 2:3

Solution: A's yearly salary = 500*12 = Rs.6000

Hence requried ratio = 6000:9000 = 2:3


19. Inverse ratio of 14 : 35 is

Answer: 5:2

Solution: Inverse ratio is 35:14,

Dividing by 7, it is 5:2


20. Find three numbers in the ratio 4 : 3 : 2 such that the sum of their squares is 261.

Answer: 12, 9, 6

Solution: Let the numbers be 4x,3x,2x.

The sum of their squares = 16x^2 + 9x^2 + 4x^2 = 261,

x^2 = 261/29 = 9, x = +3 or -3.

The numbers are 12,9,6

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