Question

10. The ratio of the present ages of A and B is 7 : 5
After 12 years the ratio between the ages of A and B
will be 5 : 4. Find the present age of B?
(b) 45 (c) 35 (d) None
a) 40​

Answer 1

Given:-

• The ratio of ages of A and B is 7 : 5
• After 12 years the ratio between the ages of A and B will be 5 : 4

To Find:-

• The present age of B

Assumption:-

• Let the ratio constant be x
• Ratio of present age of A and B = 7x : 5x

Solution:-

As it is given that after 12 years the ages of A and B wil be in the ratio 5 : 4

Hence,

After 12 years

Age of A = 7x + 12

Age of B = 5x + 12

ATQ

(7x + 12) : (5x + 12) = 5 : 4

=> (7x + 12)/(5x + 12) = 5/4

By Cross - Multiplying:-

= 4(7x + 12) = 5(5x + 12)

=> 28x + 48 = 25x + 60

=> 28x - 25x = 60 - 48

=> 3x = 12

=> x = 12/3

=> x = 4

Therefore the value of x comes as 4

Putting the value of x in the ratio whose contant we assumed to be x,

• Present age of A = 7x = 7 × 4 = 28 years
• Present age of B = 5x = 5 × 4 = 20 years

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✭ Verification:-

Let us see after 12 years do their age come in ratio of 5 : 4 or not.

After 12 years,

Age of A = 28 + 12 = 40

Age of B = 20 + 12 = 32

Ratio = 40 : 32

Let us cancel both the numerator and denominator by 8.

40 ÷ 8 = 5

32 ÷ 8 = 4

On cancelling we get the ratio as: 5 : 4

Hence the ratio of ages of A and B after 12 years is 5 : 4.

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Therefore the correct answer is option (d) None.

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