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A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 a.m. While machine P is closed at 11 a.m. and the remaining two machines complete the work. Approximately at what time will the work be finished ? 

(a) 11 : 30 a.m. 

(b) 12 noon 

(c) 12 : 30 p.m. 

(d) 1 p.m.

1 Answer

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(d) 1 p.m

(P + Q + R)’s 1 hours’ work = \(\big(\frac{1}{8}+\frac{1}{10}+\frac{1}{12}\big)\) = \(\frac{37}{120}\)

\(\therefore\) Work done by (P + Q + R) in 2 hours = 2 x \(\frac{37}{120}\) = \(\frac{37}{60}\)

Remaining work = \(\big(1-\frac{37}{60}\big)\) = \(\frac{23}{60}\)

(Q + R)’s 1 hours’ work = \(\big(\frac{1}{10}+\frac{1}{12}\big)\) = \(\frac{11}{60}\)

\(\frac{11}{60}\) of the work is done by (Q + R) in 1 hour

\(\therefore\) \(\frac{23}{60}\) of the work will be done by (Q + R) in \(\frac{23}{60}\) \(\div\)\(\frac{11}{60}\) = 2\(\frac{1}{11}\) hours = 2 hours

So, the work will be finished approximately 2 hours after 11 a.m., i.e., around 1 p.m.

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