P and Q together can complete a project in 20 days, and Q and R together can complete it in 15 days. R works twice as fast as P. How many days would Q alone take to complete the project?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 30
Write each person’s one-day work (rate) and use the link between R and P.
Let P do \(p\) of the project in a day; then R does \(2p\)
P and Q: \(\displaystyle p+q=\frac{1}{20}\)
Q and R: \(\displaystyle q+2p=\frac{1}{15}\)
Subtracting: \(\displaystyle p=\frac{1}{15}-\frac{1}{20}=\frac{4-3}{60}=\frac{1}{60}\)
\(\displaystyle q=\frac{1}{20}-\frac{1}{60}=\frac{3-1}{60}=\frac{1}{30}\)
Q alone would take 30 days.
Why the other options are incorrect
Option (1) 20 — Incorrect. Then P\(=\frac{1}{20}-\frac{1}{20}=0\): P would do no work at all, so R could not be twice as fast as P.
Option (2) 24 — Incorrect. Then P\(=\frac{1}{20}-\frac{1}{24}=\frac{1}{120}\) and R\(=\frac{1}{15}-\frac{1}{24}=\frac{3}{120}\): R would be 3 times as fast as P, not twice.
Option (4) 60 — Incorrect. Then P\(=\frac{1}{20}-\frac{1}{60}=\frac{1}{30}\) and R\(=\frac{1}{15}-\frac{1}{60}=\frac{1}{20}\): R would be only 1.5 times as fast as P, not twice.