Question

The ages of Akbar and Rahim are in the ratio of 3:5. Five years later the sum of their ages will be 50 years. What are their present ages?

Answer 1

Answer:

Given :-

• The ages of Akbar and Rahim are in the ratio of 3 :5.
• Five years later the sum of their ages will be 50 years.

To Find :-

• What are their present ages.

Solution :-

Let,

$\mapsto \rm{\bold{Present\: age\: of\: Akbar =\: 3x\: years}}$

$\mapsto \rm{\bold{Present\: age\: of\: Rahim =\: 5x\: years}}$

$\clubsuit$ Five years later :

$\leadsto \rm{Age\: of\: Akbar =\: (3x + 5)\: years}$

$\leadsto \rm{Age\: of\: Rahim =\: (5x + 5)\: years}$

According to the question,

$\implies \sf (3x+ 5) + (5x + 5) =\: 50$

$\implies \sf 3x + 5 + 5x + 5 =\: 50$

$\implies \sf 3x + 5x + 5 + 5 =\: 50$

$\implies \sf 8x + 10 =\: 50$

$\implies \sf 8x =\: 50 - 10$

$\implies \sf 8x =\: 40$

$\implies \sf x =\: \dfrac{\cancel{40}}{\cancel{8}}$

$\implies \sf \bold{\purple{x =\: 5\: years}}$

Hence, the required ages of Akbar and Rahim are :

$\mapsto \sf\bold{\green{Present\: age\: of\: Akbar\: :-}}$

$\longrightarrow \sf 3x\: years$

$\longrightarrow \sf 3 \times 5\: years$

$\longrightarrow \sf\bold{\red{15\: years}}$

$\mapsto \sf\bold{\green{Present\: age\: of\: Rahim\: :-}}$

$\longrightarrow \sf 5x\: years$

$\longrightarrow \sf 5 \times 5\: years$

$\longrightarrow \sf\bold{\red{25\: years}}$

$\therefore$ The present age of Akbar and Rahim is 15 years and 25 years respectively.

Answer 2

Answer

We know that,

The ratio of two friends Akbar and Rahim are in the ratio of 3:5.

The sum of their ages will be 50 years, five years later.

In this question, we are asked to find the present ages of those both.

According to the question,

$\sf \dashrightarrow Akbar : Rahim = 50$

$\sf \dashrightarrow 3y + 5 : 5y + 5 = 50$

$\sf \dashrightarrow 3y + 5 + 5y + 5 = 50$

$\sf \dashrightarrow 8y + 5 + 5 = 50$

$\sf \dashrightarrow 8y + 10 = 50$

$\sf \dashrightarrow 8y = 50 - 10$

$\sf \dashrightarrow 8y = 40$

$\sf \dashrightarrow y = \dfrac{40}{8}$

$\sf \dashrightarrow y = 5$

So, the present ages of Akbar and Rahim are,

Present age of Akbar :

$\sf \dashrightarrow 3y = 3(5)$

$\sf \dashrightarrow 15 \: \: years$

Present age of Rahim :

$\sf \dashrightarrow 5y = 5(5)$

$\sf \dashrightarrow 25 \: \: years$

Hence, the present ages of Akbar and Rahim are 15 and 25 years respectively.