Q) 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 work. Approximately at what time will the work (to print one lakh books) be finished?

a) 11:30 AM                     b) 12:00 Noon             c) 12:30 PM                     d) 1 PM

Ans:

P’s 1 hr work = 1/8

Q’s 1 hr work = 1/10

R’s 1 hr work = 1/12

∴ (P + Q + R)’s 1 hr work = 1/8 + 1/10 + 1/12 = 37/120

∴ (P + Q + R)’s 2 hrs work = 2 x 37/120 = 74/120

∴ Balance work = 1 – 74/120 = 46/120

Also (Q + R)’s 1 hr work = Q’s 1 hr work + R’s 1 hr work

= 1/10 + 1/12 = 11/60

Time taken by (Q + R) to do 11/60 work = 1 hr

Time taken by (Q + R) to do 46/120 work = 1 x 46/120 / (11/60) = 23/11 = 2 hrs 5 mins.

This time taken after 11 am, hence work finished by 11:00 + 2:05 = 1:05 pm

Hence, Answer is [D].

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