Question : 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:
Option 1: 72
Option 2: 60
Option 3: 84
Option 4: 48
Correct Answer: 84
Solution :
Let the present ages A and B be 3$x$ and 4$x$
Present age of ratio = 3 : 4
Before 12 years the ratio of ages A and B = 2 : 3
According to the question,
⇒ $\frac{(3x - 12)}{4x - 12)}$ = $\frac{2}{3}$
⇒ $3(3x − 12) = 2(4x − 12)$
⇒ $9x − 36 = 8x − 24$
⇒ $x − 36 = −24$
⇒ $x$ = 12
A's present age = 3$x$ = 3 × 12 = 36 years
B's present age = 4$x$ = 4 × 12 = 48 years
So, the sum of the present ages of A and B = 36 + 48 = 84 years
Hence, the correct answer is 84.
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