Question 1

P can do some work in 4 hours. Q and R together can finish it in 3 hours while P and R can do
it in 2 hours. How long will Q take to complete it, if he works alone?

Solution

P’s one hour’s work

$$ = \frac{1}{4}$$
(Q + R)’s one hour’s work

$$ = \frac{1}{3}$$
(P + R)’s one hour’s work

$$ = \frac{1}{2}$$
∴ R’s one hour’s work

$$ = \frac{1}{2} - \frac{1}{4} = \frac{2-1}{4} = \frac{1}{4}$$
Q’s one hour’s work

$$ = \frac{1}{3} - \frac{1}{4} = \frac{4-3}{12} = \frac{1}{12}$$

Hence Q alone can do the work in 12 hours,

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P can do some work in 4 hours. Q and R together can finish it in 3 hours while P and R can doit in 2 hours. How long will Q take to complete it, if he works alone?