Question

The present ages of Rafi and fathima are in the ratio 7:5. Ten years later the ratio of their ages will be 9:7. find their present ages.​

Answer 1

Solution :

Since the presen ratios of ages of Rafi and Fathima is 7:5,

We may take, Rafi's age to be 7x and the Fathima's age to be 5x

(Note that ratio of 7x and 5x is 7x: 5x and which is same as 7:5)

After 10 years Rafî's age = 7x + 10

and Fathima's age = 5x + 10

After 10 years, the ratio of Rafi's age and Fathima's age is 7x + 10 : 5x + 100

But according to the given data this ratio is equal to 9 : 7

7x + 10 : 5x + 10 = 9 : 7

ie., 7 (7x + 10) = 9 (5x + 10)

49 x+ 70 =45 x+90.

The above equation is 49x + 70 =45x + 90

49x - 45x = 90 - 70 (Transposing 70 to RHS and 45x to LHS)

4x= 20

x = 20/4

=> x = 5

=> Raff's age = 7x = 7 x 5 = 35 years

Fathima's age = 5x = 5 x 5 = 25 years