Question
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 work. Approximately at what time will the work (to print one lakh books) be finished?Solution
The efficiency of P is 1/8 The efficiency of Q is 1/10 The efficiency of R is 1/12 Work done by P + Q + R in one hour ⇒ 1/8 + 1/10 + 1/12 = (15 + 12 + 10)/120 ⇒ 37/120 P, Q and R work for two hours 9 A.M to 11 A.M ⇒ 37/120 × 2 = 37/60 Remaining work is ⇒ 1 - 37/60 = 23/60 ⇒ Work done by Q and R in an hour ⇒ 1/10 + 1/12 = 11/60 Now time taken to complete the remaining work ⇒ (23/60) ÷ (11/60) ⇒ (23/60) × (60/11) = 23/11 ≈ 2 hours So add 2 hours in 11 A.M we get 1 P.M ∴ The correct answer is 1 P.M
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