If 40% of P = 0.5 of Q = 1/8 of R, find P : Q : R.

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1. Let the common value be $k$. So $0.4P = 0.5Q = \frac{1}{8}R = k$.
2. Solve for each: $P=\dfrac{k}{0.4}=\dfrac{5}{2}k$, $Q=\dfrac{k}{0.5}=2k$, $R=\dfrac{k}{1/8}=8k$.
3. Form the ratio: $P:Q:R=\dfrac{5}{2}k:2k:8k$. Multiply all by 2 to clear the fraction.
4. We get $5k:4k:16k$. So $P:Q:R=5:4:16$. **Answer (a).**
FINAL_ANSWER: a

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