Four pipes A,B, C and D can fill a cistern in 20,25, 40 and 50 hours respectively.The first pipe A was opened at 6:00 am, B at 8:00 am, C at 9:00 am and D at 10:00 am. when will the Cistern be full?
A. 4:18 pm
B. 3:09 pm
C. 12:15 pm
D. 11:09 am
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Work Rate of A = 100/20 = 5% per hour.
Work rate of B = 100/25 = 4% per hour.
Work rate of C = 100/40 = 2.5% per hour.
Work rate of D = 100/50 = 2% per hour.
Cistern filled till 10 am by A, B and C,
= (4 *5 + 2*4 + 2.5)
= 30.5%.
Rest cistern to be filled = 100 - 30.5 = 69.5%.
Now, cistern is filled by A, B, C and D in
= 69.5/(5 +4+2.5+2)
= 69.5/13.5
= 5.29 hours.
So, it will take 5.14 hour to be filled after 10 am.
Thus, time would be 3.09 pm.