P can do a task in 30 days. Q is 50% more efficient than P, and R can do the same work in 10 days less than Q. If R and Q start the task together and after X days they leave the task, and P completes the remaining work in (X + 8) days, then find the value of X.

Correct answer: 4

Solution

P’s rate is 1/30 per day. Q is 50% more efficient, so Q’s time is 20 days. R takes 10 days less than Q, so R takes 10 days. Their combined rate is then used with P’s finishing time to form an equation in X, which gives X = 4.

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