Q) A cistern has two pipes one can fill it with water in 16 hours and other can empty it in 10 hours. In how many hours will the cistern be emptied if both the pipes are opened together when 1/5th of the cistern is already filled with water?
a) 11.4 hours b) 3.66 hours c) 5.33 hours d) 8.33 hours
Ans:
Work done by 1st pipe P1 in one hour = 1/16
Work done by 2nd pipe P2 in one hour = -1/10
∴ Work done by P1 and P2 together in one hour = 1/16 – 1/10 = – 3/80
(Here negative sign is indicator of the cistern tank is being emptied.)
It means, time taken by both pipes together to empty 3/80 tank = 1 hour
∴ time taken to by both pipes together to empty full tank = 1/(3/80) = 80/3 hours
∴ time taken to by both pipes together to empty 1/5th of the tank
= 80/3 x 1/5 = 16/3 = 5.33 hours
Hence, Answer is [C]
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