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 :

• Present Ages of Virat and Sachin are in the ratio 5:9 .
• After 3 years their ages will be in the ratio 3:5 .

To Find :

• Present Age of Virat .

Solution :

$\longmapsto\tt{Let\:Present\:Age\:of\:Virat\:be=5x}$

$\longmapsto\tt{Let\:Present\:Age\:of\:Sachin\:be=9x}$

After 3 years :

$\longmapsto\tt{Present\:Age\:of\:Virat=5x+3}$

$\longmapsto\tt{Present\:Age\:of\:Sachin=9x+3}$

A.T.Q :

$\longmapsto\tt{\dfrac{5x+3}{9x+3}=\dfrac{3}{5}}$

$\longmapsto\tt{5(5x+3)=3(9x+3)}$

$\longmapsto\tt{25x+15=27x+9}$

$\longmapsto\tt{25x-27x=9-15}$

$\longmapsto\tt{-2x=-6}$

$\longmapsto\tt{x=\cancel\dfrac{-6}{-2}}$

$\longmapsto\tt\bf{x=3}$

Therefore :

$\longmapsto\tt{Present\:Age\:of\:Virat=5(3)}$

$\longmapsto\tt\bf{15\:yrs}$

$\longmapsto\tt{Present\:Age\:of\:Sachin=9(3)}$

$\longmapsto\tt\bf{27\:yrs}$

Answer 2

$\huge \bf Given$

Ratio of present age of Virat and Sachin = 5:9

After 3 yeas the ratio will be 3:5

$\huge \bf To \: Find$

Virat's present age

$\huge \bf Solution$

Let the present age ratio be 5y and 9y Now,

After 3 years

$\sf \dfrac{5y+ 3}{9y + 3} = \dfrac{3}5$

By Cross Multiplication

3(9y + 3) = 5(5y + 3)

27y + 9 = 25y + 15

27y - 25y = 15 - 9

2y = 6

y = 6/2

y = 3

Present age of Virat is 5(3) = 15 years