Correct Answer - Option 4 : 1 : 30 p.m.
Given:
In a press, there are three types of printing machines, P, Q and R. Machine P can print 10,000 pages in 8 hours, machine Q can finish the same task in 10 hours and machine R can finish the same task in 15 hours. All the three machines start the work at 9 : 00 a.m. Machine P breaks down at 11 : 00 a.m. and machines Q and R finish the task.
Concept used:
Time and work
Calculation:
Time taken by three different machines
P : Q : R = 8 : 10 : 15
Take LCM of (8, 10, 15) which is 120
Total work = 120 unit
Efficiency of P = 120/8 = 15 hours
Efficiency of Q = 120/10 = 12 hours
Efficiency of R = 120/15 = 8 hours
They all started the work at 9 : 00 am and P breaks down at 11 : 00 am
They all worked together for 2 hours
Total work completed
⇒ (15 + 12 + 8) × 2 = 70 unit
Remaining work
⇒ 120 - 70 = 50 unit
Remaining work will be completed by machine Q and R
Remaining work
⇒ \(\frac{{50}}{{12 + 8}} = \frac{5}{2} = 2.5\ hrs\)
Total time taken by three machines
⇒ 11 : 00 am + 2.5 hrs = 1 : 30 p.m.
