Question

The ratio between the present ages of A and B is 9:10. After 8 years the ratio of their

ages will become 11:12. Find the present age of A.​

Answer 1

A’s age = 9x, B’s age = 10x

After 8 years,

9x + 8 : 10x + 8 = 11 : 12

12 (9x + 8) : 11 (10x + 8)

108x +96 = 110x + 88

110x – 108x = 96 – 88

2x = 8

x = 4

A’s present age = 4 × 9 = 36

Answer 2

Answer:

The present age of A is 36 years.

Step-by-step explanation:

Given that,

The ratio between the present ages of A and B is 9:10. After 8 years the ratio of their ages will become 11:12.We are required to find the present age of A.

Let the present ages of A and B be x and y.Hence we write

$\frac{x}{y} =\frac{9}{10} = > 10x-9y=0--- > (1)$

Also given that,

The ratio of ages after 8 years would be 11:12.Therefore,we write

$\frac{x+8}{y+8} =\frac{11}{12} = > 12x+96=11y+88\\= > 12x-11y+8=0-- > (2)$

Solving both the equations,we get the solutions as follows

$x=36,y=40$

Therefore,the present age of A is found to be 36 years.

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