Question : A piece of work can be completed by P and Q together in 24 days, and the same piece of work can be completed by R alone in 60 days. If P and R together can do the same work in 36 days, then find the time taken by Q to complete this piece of work alone.
Option 1: $8\frac{4}{5}$days
Option 2: $29\frac{9}{13}$days
Option 3: $3\frac{6}{7}$days
Option 4: $32\frac{8}{11}$days
Correct Answer: $32\frac{8}{11}$days
Solution :
One day work of P and Q together $= \frac{1}{24}$........................(equation 1)
One day work of R $= \frac{1}{60}$........................(equation 2)
One day work of P and R together $= \frac{1}{36}$........................(equation 3)
From equation 2 and 3, we get:
One day work of P $= \frac{1}{36}-\frac{1}{60}=\frac{1}{90}$........................(equation 4)
From equation 1 and 4, we get:
$\therefore$ One day work of Q $= \frac{1}{24}-\frac{1}{90}=\frac{11}{360}$
Thus the work can be completed by Q alone $= \frac{360}{11}=32\frac{8}{11}$
Hence, the correct answer is $32\frac{8}{11}$.
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