Question

Two number are in the ratio 7: 11. If 7 is added to each of the numbers, the ratio becomes 2: 3. Find the numbers.

Answer 1

Let the numbers are 7x and 11x,

Then,

= (7x + 7): (11x + 7) = 2: 3

= (7x + 7)/ (11x + 7) = (2/3)

By cross multiplication,

= 3 × (7x + 7) = 2 × (11x + 7)

= 21x + 21 = 22x + 14

Transposing 21x to RHS and 14 to LHS

= 21 – 14 = 22x – 21

= x = 7

Hence the numbers are 7x = 7 × 7 = 49

11x = 11 × 7 =77