P can build a wall in the same time in which Q and R together can do it. If P and Q together could do it in 30 days and R alone in 40 days, in what time could Q alone do it?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 240 days
A person who finishes a job in \(n\) days does \(\frac{1}{n}\) of it in one day, and the work of people working together is added. P takes the same time as Q and R together, so P’s one-day work equals Q’s plus R’s.
P and Q together: \(\displaystyle P+Q=\frac{1}{30}\) (1)
R alone: \(\displaystyle R=\frac{1}{40}\), and \(P=Q+R\) (2)
Finding Q (putting \(P=Q+R\) from (2) into (1)):
\(\displaystyle 2Q+\frac{1}{40}=\frac{1}{30}\)
\(\displaystyle 2Q=\frac{1}{30}-\frac{1}{40}=\frac{4-3}{120}=\frac{1}{120}\)
\(\displaystyle Q=\frac{1}{240}\), so Q alone takes 240 days