Question

The ratio of the ages of two brothers is 3:2.In eight years, the ratio of their ages becomes 5:4 . Find their present ages​

Answer 1

Answer:

Given :-

• The ratio of the ages of two brothers is 3 : 2.
• In eight years, the ratio of their ages becomes 5 : 4.

To Find :-

• What is their present ages.

Solution :-

Let,

$\mapsto \bf Present\: Age_{(1^{st}\: Brother)} =\: 3x\: years$

$\mapsto \bf Present\: Age_{(2^{nd}\: Brother)} =\: 2x\: years$

☆ After 8 years :

$\mapsto \sf Age_{(1^{st}\: Brother)} =\: (3x + 8)\: years$

$\mapsto \sf Age_{(2^{nd}\: Brother)} =\: (2x + 8)\: years$

According to the question :

$\bigstar$ After 8 years, their ratio of their ages becomes 5 : 4.

So,

$\footnotesize \implies \bf \bigg\{Age_{(1^st\: Brother)}\bigg\} : \bigg\{Age_{(2^{nd}\: Brother)}\bigg\} =\: 5 : 4$

$\implies \sf (3x + 8) : (2x + 8) =\: 5 : 4$

$\implies \sf \dfrac{3x + 8}{2x + 8} =\: \dfrac{5}{4}$

By doing cross multiplication we get,

$\implies \sf 4(3x + 8) =\: 5(2x + 8)$

$\implies \sf 12x + 32 =\: 10x + 40$

$\implies \sf 12x - 10x =\: 40 - 32$

$\implies \sf 2x =\: 8$

$\implies \sf x =\: \dfrac{\cancel{8}}{\cancel{2}}$

$\implies \sf\bold{\purple{x =\: 4}}$

Hence, the required present ages of two brothers are :

❒ Present Age Of First Brother :

$\dashrightarrow \sf Present\: Age_{(1^{st}\: Brother)} =\: 3x\: years$

$\dashrightarrow \sf Present\: Age_{(1^{st}\: Brother)} =\: (3 \times 4)\: years$

$\dashrightarrow \sf\bold{\red{Present\: Age_{(1^{st}\: Brother)} =\: 12\: years}}$

❒ Present Age Of Second Brother :

$\dashrightarrow \sf Present\: Age_{(2^{nd}\: Brother)} =\: 2x\: years$

$\dashrightarrow \sf Present\: Age_{(2^{nd}\: Brother)} =\: (2 \times 4)\: years$

$\dashrightarrow \sf\bold{\red{Present\: Age_{(2^{nd}\: Brother)} =\: 8\: years}}$

$\therefore$ The present age of two brothers are 12 years and 8 years respectively.