Question

The ratio of present ages of Virat and Sachin is 5 : 9. Three years hence ratio of their ages will be 3 : 5. Find Virat's present age?​

Answer 1

Given :

The ratio of present ages of Virat and Sachin is 5 : 9. Three years hence ratio of their ages will be 3 : 5.

To find :

Find Virat's present age.

Solution :

Let the present ages of Virat and Sachin be '5x' and '9x' respectively.

Now according to question :

⇒ (5x + 3) : (9x + 3) = 3 : 5

⇒ (5x + 3)/(9x + 3) = 3/5

⇒ 5(5x + 3) = 3(9x + 3)

⇒ 25x + 15 = 27x + 9

⇒ 27x - 25x = 15 - 9

⇒ 2x = 6

⇒ x = 6/2

⇒ x = 3

∴ Present age of Virat = 5x

⇒ Present age of Virat = 5 × 3

∴ Present age of Virat = 15 years.

Answer 2

Answer:

Given :-

• The ratio of present ages of Virat and Sachin is 5 : 9. Three years ago the ratio of their ages will be 3 : 5.

To Find :-

• What is the present age of Virat.

Solution :-

Let, the present age of Virat is 5x

And, the present age of Sachin will be 9x

$\mapsto$ Three years ago,

Age of Virat = 5x + 3

And, the age of Sachin will be 9x + 3

According to the question,

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

By doing cross multiplication we get,

⇒ $\sf 3(9x + 3) =\: 5(5x + 3)$

⇒ $\sf 27x + 9 =\: 25x + 15$

⇒ $\sf 27x - 25x =\: 15 - 9$

⇒ $\sf 2x =\: 6$

⇒ $\sf x =\: \dfrac{\cancel{6}}{\cancel{2}}$

➠ $\sf\bold{\purple{x =\: 3}}$

Hence, the required ages are,

✧ Present age of Virat = 5x = 5(3) = 15 years

✧ Present age of Sachin = 9x = 9(3) = 27 years

$\therefore$ The present age of Virat is 15 years .