Question

The ages of Rahul and Laxmi arc in the ratio 5:7. Four years later, the sum of their ages will be 56 years. What are their present ages’?

Answer 1

The ratio of ages of Rahul and Lakshmi = 5:7 

Let their ages be 5x, 7x say. 

After 4 years Rahuls agt. = 5x + 4

After 4 years Lakshmis age = 7x + 4

According to the sum, 

After 4 years the sum of their ages = 56 

⇒ (5x + 4) + (7x + 4) = 56 

⇒ 12x + 8 = 56 

⇒ 12x = 56 – 8 = 48 

⇒ x = \(\frac{48}{12}\) = 4 

∴ x = 4 

∴ Rahuls present age 

= 5x = 5 × 4 = 20 years 

∴ Lakshmi’s present age 

= 7x = 7 × 4 = 28 years