Question

The ages of Leena and Heena are in the ratio 7:5 . Ten years hence, the ratio of their ages will be 9:7. find their present ages.

Answer 1

let Leena's present age be 7x years and Heena's present age be 5x years            
 After 10 years,
Leena's age=7x+10
Heena's age=5x+10
7x+10+5x+10=9x+7x
20=16x-12x
20=4x
x=5

Leena's present age=7x=7×5=35
Heena's present age=5×5=25

Answer 2

The ratio of the present ages of Leena and Heena = 7:5
Let the age of Leena be 7x years and Heena be 5x years
Ten years later their ages will be 7x +10 years and 5x + 10 years
but the ratio of their ages after ten years is given as 9:7
let their ages be 9x and 7x
∴9x + 7x = 7x + 10 + 5x + 10  
⇒9x = -7x + 7x + 10 + 5x + 10
⇒9x -5x = 10 + 10
⇒4x = 20
⇒x = 20/4 = 5
∴The age of Leena = 7x = 7* 5 = 35 years
And Heena`s age = 5x = 5* 5 = 25 years.