Question

опренапре
• 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?
2​

Answer 1

Answer

Rafi's age = 35 years

Fathima's age = 25 years

Explanation

Since the present ratio 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 Rafi's age 7x + 10

And Fathima's age 5x+!0

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

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)

49x + 70 = 45x + 90

Did you notice that in the above equation we have algebraic expressions on both sides. Note let us learn how to solve such equations. The above equation is 49x + 70 = 45x + 90

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

.:4x = 20

.'. x = 20÷4

Therefore Rafi's age = 7x = 7 x 5 = 35 years

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