Question

The ratio of the present ages of P and Q is 3:4. Five years ago, the ratio of their ages was 5:7. Find their present ages.

• A. 30 and 40 years
• B. 24 and 32 years
• C. 12 and 16 years
• D. 18 and 24 years

Hint:

Set present ages as 3k and 4k, then use the five-years-ago ratio to find k.

Answer 1

The Correct Option is A

Check each option by testing the ratio five years ago.
For 30 and 40, ages five years back were 25 and 35, and $25/35 = 5/7$. This matches the given condition.
For 24 and 32, five years back the ratio is $19/27$, not $5/7$.
For 12 and 16, the ratio is $7/11$, not $5/7$.
For 18 and 24, the ratio is $13/19$, not $5/7$.
Only the first pair works.
\[\boxed{30 \text{ and } 40 \text{ years}}\]