Question

Present ages of Rohit and Mayank are in the ratio 11:8. Eight years later the ratio of their ages will be 5:4. Find their present ages

Answer 1

Let's say the present ages of Rohit and Mayank are:

11x and 8x. (where x is a positive value)

Their ages 8 years later will be :

11x + 8 and 8x + 8

Now these are in the ratio of 5:4. Therefore :

$(11x + 8) \div (8x + 8) = 5 \div 4 \\ 4(11x + 8) = 5(8x + 8) \\ 44x + 32 = 40x + 40 \\ 4x = 8 \\ x = 2$
So Rohit's current age is 11x = 22 years
And Mayank's current age is 8x = 16 years

Answer 2

Given :

The present ages of Rohit and Mayank are in the ratio 11 : 8 .

8 years later the sum of their ages will be 54 years.

To Find :

Present Age of Rohit and Mayank .

Solution :

$\longmapsto\tt{Let\:Present\:age\:of\:Rohit\:be=11x}$

$\longmapsto\tt{Let\:Present\:age\:of\:Mayank\:be=8x}$

After 8 years :

$\longmapsto\tt{Age\:of\:Rohit=11x+8}$

$\longmapsto\tt{Age\:of\:Rohit=8x+8}$

A.T.Q :

$\longmapsto\tt{11x+8+8x+8=54}$

$\longmapsto\tt{19x+16=54}$

$\longmapsto\tt{19x=54-16}$

$\longmapsto\tt{19x=38}$

$\longmapsto\tt{x=\cancel\dfrac{38}{19}}$

$\longmapsto\tt\bf{x=2}$

Value of x is 2 .

Therefore :

$\longmapsto\tt{Present\:Age\:of\:Rohit=11(2)}$

$\longmapsto\tt\bf{22\:yrs}$

$\longmapsto\tt{Present\:Age\:of\:Mayank=8(2)}$

$\longmapsto\tt\bf{16\:yrs}$