Two numbers are such that the ratio between them is 4 : 7. If each is increased by 4, the ratio becomes 3 : 5. The larger number is:

Question: Two numbers are such that the ratio between them is 4 : 7. If each is increased by 4, the ratio becomes 3 : 5. The larger number is:

Solution:
Let the numbers be 4x and 7x.

According to the question,
(4x + 4)/(7x + 4) = 3/5
⇒ 5(4x + 4) = 3(7x + 4)
⇒ 20x + 20 = 21x + 12
∴ x = 8

∴ Larger number = 7x
= 7 × 8
= 56