Question

The ratio of the ages of two boys is 3:4. After 3 years, the ratio will be 4:5.The ratio of their ages after 21 years will be

A) 14:17 B) 17:19 C) 11:12 D) 10:11

Answer 1

LET THE AGES OF BOYS BE 3x AND 4x YEARS RESPECTIVELY.

AFTER THREE YEARS AGE OF BOYS WILL BE 3x+3 AND 4x+3 YEARS RESPECTIVELY.

$\longrightarrow \frac{3x + 3}{4x + 3} = \frac{4}{5} \\\\ \longrightarrow5(3x + 3) = 4(4x + 3) \\ \\ \longrightarrow15x + 15 = 16x + 12 \\ \\ \longrightarrow 16x - 15x = 15 - 12 \\ \\ \longrightarrow \: x = 3$

RATIO AFTER 21 YEARS

= 3x+21 : 4x+21

= 9+21 : 12+21

= 30 : 33

= 10 : 11