The ratio of ages of A and B is 3 : 11. After 3 years the ratio becomes 1:3. Wha

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Question
The ratio of ages of A and B is 3 : 11. After 3 years the ratio becomes 1:3. What are the ages of A and B?
Options
A. 9 years, 33 years
B. 10 years, 40 years
C. 9 years, 27 years
D. None of these

Correct Answer

9 years, 33 years

Explanation

Let us assume the ages of A and B be 3x and 11x years; then
After 3 years the ages of A and B will be 3x + 3 and 11x + 3.
According to question,
After 3 years the ratio of the ages becomes 1: 3,
(3x + 3)/(11x + 3) = 1/3
? 3 (3x + 3) = 1 (11x + 3)
? 9x + 9 = 11x + 3
? 2x = 6
? x = 3
Hence, their present age, 3x = 3 x 3 = 9 years; 11x = 11 x 3 =33 years