Question

If the present ages of A and B are in the ratio 9:4 and seven years hence,the ratio of their ages will be 5:3, then find their present ages

Answer 1

Solutions :-

Given :
The present ages of A and B are in the ratio 9 : 4
After seven years,
The ratio of their ages will be 5 : 3

Let the present age of A and B be 9x and 4x respectively.

According to the question,

$= > \frac{9x + 7}{4x + 7} = \frac{5}{3} \\ \\ = > 3( 9x + 7) = 5(4x + 7) \\ \\ = > 27x + 21 = 20x + 35 \\ \\ = > 27x - 20x = 35 - 21 \\ \\ = > 7x = 14\\ \\ = > x = \frac{14}{7} = 2$

Hence,
Present age of A = 9x = 9 × 2 = 18 years
Present age of B = 4x = 4 × 2 = 8 years

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✯ @shivamsinghamrajput ✯

Answer 2

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Let their ages be 9p and 4p.

By the problem,

$\bf\huge\frac{9p\: +\: 7}{4p\:+\:7} = \frac{5}{3}$

3(9p + 7) = 5(4p + 7)

27p + 21 = 20p + 35

27p - 20p = 35 - 21

7p = 14

p = $\bf\huge\frac{14}{7}$

p = 2

A's age = 9p = 9 × 2 = 18

B's age = 4p = 4 × 2 = 8

A is 18 years old and B is 8 years old.