P and Q together can do a piece of work in 60 days. Q and R together can do it in 120 days. P and R together can do it in 90 days. In what time can Q alone do the same work?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 144 days
When a job is measured in units, each person’s one-day work is a number of units, and the work of people working together is added.
One-day work of each pair (assuming the whole work to be 360 units, the LCM of 60, 120 and 90):
\(P+Q=360\div60=6\) units (1)
\(Q+R=360\div120=3\) units (2)
\(P+R=360\div90=4\) units (3)
All three together (adding (1), (2) and (3), each person counted twice):
\(2(P+Q+R)=13\)
\(P+Q+R=6.5\) units (4)
Q alone (subtracting (3) from (4), P and R cancel):
\(Q=6.5-4=2.5\) units a day
Days \(=360\div2.5=144\)