Q12 of 80 Page 42

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

The ratio of the ages of Rahul and Laxmi = 5:7

Let the common multiple be x.


∴ Rahul’s present age = 5x years.


Laxmi’s present age = 7x years.



The sum of their ages four years later = 56 years.


According to the given condition,


5x + 4 + 7x + 4 = 56


⇒ 12x + 8 = 56


⇒ 12x = 56 – 8 (Transposing 8 to RHS)


12x = 48


⇒ x = (Transposing 12 to RHS)


x = 4


Rahul’s present age = 5x = 5 × 4 = 20 years.


Laxmi’s present age = 7x = 7 × 4 = 28 years.


∴ The present ages of Rahul and Laxmi are 20 years and 28


years respectively.


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