The present ages of A and B are in the ratio 3 : 4. Twelve years ago, their ages were in the ratio 2 : 3. The sum of the present ages of A and B (in years) is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 84.
Twelve years ago, their ages were in the ratio 2 : 3 = 2x : 3x
Present age of A and B = (2x + 12) : (3x + 12)
The present ages of A and B are in the ratio 3 : 4
Now, according to the question
⇒ (2x + 12)/(3x + 12) = 3/4
⇒ 4(2x + 12) = 3(3x + 12)
⇒ 8x + 48 = 9x + 36
⇒ 9x - 8x = 48 - 36
⇒ x = 12
Present age of A = 3x = 36 years
Present age of B = 4x = 48 years
The sum of the present ages of A and B = 36 + 48 = 84 years