Question

The present ages of Albert and Salim is in ratio 5: 9. Five years hence the ratio of their ages will be 3: 5. Find their present ages.

Answer 1

Answer:

$\huge\sf\red{A}\orange{N}\green{S}\blue{W}{E}\pink{R}$

$\frac{5}{9} + 5 = \frac{3}{5}$

Step-by-step explanation:

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Answer 2

Answer:

Given :-

• The present ages of Albert and Salim is in the ratio of 5 : 9.
• Five years hence, the ratio of their ages will be 3 : 5.

To Find :-

• What is their present ages.

Solution :-

Let,

$\mapsto \bf Present\: Age_{(Albert)} =\: 5x\: years$

$\mapsto \bf Present\: Age_{(Salim)} =\: 9x\: years$

☆ Five years hence :

$\leadsto \sf Age_{(Albert)} =\: (5x + 5)\: years$

$\leadsto \sf Age_{(Salim)} =\: (9x + 5)\: years$

According to the question :

$\bigstar$ Five years hence, the ratio of their ages will be 3 : 5.

So,

$\footnotesize \implies \bf \bigg\{Age_{(Albert)}\bigg\} : \bigg\{Age_{(Salim)}\bigg\} =\: 3 : 5$

$\implies \sf (5x + 5) : (9x + 5) =\: 3 : 5$

$\implies \sf \dfrac{5x + 5}{9x + 5} =\: \dfrac{3}{5}$

By doing cross multiplication we get,

$\implies \sf 3(9x + 5) =\: 5(5x + 5)$

$\implies \sf 27x + 15 =\: 25x + 25$

$\implies \sf 27x - 25x =\: 25 - 15$

$\implies \sf 2x =\: 10$

$\implies \sf x =\: \dfrac{\cancel{10}}{\cancel{2}}$

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

Hence, the required present ages of Albert and Salim are :

$\footnotesize \dashrightarrow \sf\bold{\red{Present\: Age_{(Albert)} =\: 5x\: years =\: (5 \times 5)\: years =\: 25\: years}}$

$\footnotesize \dashrightarrow \sf\bold{\red{Present\: Age_{(Salim)} =\: 9x\: years =\: (9 \times 5)\: years =\: 45\: years}}$

$\therefore$ The present age of Albert is 25 years and the present age of Salim is 45 years .