Discussion
Eighteen years ago, the ratio of P's age to Q's age was 8:13. Their present age ratios are 5:7. Then the present age of P is
Answer: A
P's present age is 50 years.
Let the present ages be \(5x\) and \(7x\). Eighteen years ago they were in the ratio 8:13.
\[ \begin{aligned} \frac{5x - 18}{7x - 18} &= \frac{8}{13} \\ 65x - 234 &= 56x - 144 \\ 9x &= 90,\ x = 10 \end{aligned} \]
So P is \(5 \times 10 = 50\) and Q is 70. Check: 18 years ago they were 32 and 52, and \(32:52 = 8:13\). 70 years is Q's age, not P's.
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