Question

5 years ago ratio between the ages of A and B was 2:3.6 years hence the ratio of their age will be 3:4.find their present age​

Answer 1

Correct Question:-

The ratio between the ages of A and B at present are 2 : 3. After 6 years the ratio of their ages will be 3 : 4. Then what's their present age.

To Find:-

• Find the present ages.

Given:-

Let the respective ages be 2x and 3x.

The ratio of their ages after 6 years will be

️$\sf \implies\dfrac{2x+6}{3x+6} = \dfrac{3}{4}$

️$\sf \implies\ \: 4( \: 2x \: + \: 6 \: ) \: = \: 3( \: 3x \: + \: 5 \: )$

$\sf \implies\ \: 8x \: + \: 24 \: = \: 9x \: + \: 18 \:$

$\sf \implies\ \: 9x \: - \: 8x \: = \: 24 \: - \: 18 \:$

️$\implies\boxed{\sf \ \: x \: = \: 6 \: \: \: }$

So,

Present age:-

️ ➭ The present age of A is 2x = 2(6) => 12

️ ➭ The present age of B is 3x = 3(6) = 18

Answer 2

Answer:

Given :-

• 5 years ago ratio between the ages of A and B was 2:3
• After 6 years hence the ratio of their age will be 3:4

To Find :-

Present age

SoluTion :-

Let the present age of A and B be x

$\tt \: \dfrac{2x + 6}{3x + 6} = \dfrac{3}{4}$

$\tt \: 4(2x + 6) = 3(3x + 6)$

$\tt \: 8x + 24 = 9x + 18$

$\tt \: 9x - 8x = 24 - 18$

$\tt \: x = 24 - 18$

$\tt \: x = 6$

Present age :-

The present age of A is2x = 2(6) = 12

The present age of B is 3x = 3(6) = 18