3 pipes A, B and C can till a cistern is 7 hours. After working for 2 hours C is closed A and B required 10 hours more to fill it. How long will C take to fill the cistern alone?
Answers
Given :- 3 pipes A, B and C can till a cistern is 7 hours. After working for 2 hours C is closed A and B required 10 hours more to fill it. How long will C take to fill the cistern alone ?
Solution :-
given that,
→ (A + B + C) can fill the pipe in = 7 hours.
So,
→ in 1 hour (A + B + C) will fill = (1/7) unit of water .
then,
→ for first 2 hours (A + B + C) will fill = 2 * (1/7) = (2/7) unit of water .
Now,
→ Left quantity to be filled = 1 - (2/7) = (3/7) unit of water .
given that, (A + B) the remaining cistern in 10 hours .
So,
→ in 10 hours (A + B) fill = (3/7) unit of water .
→ in 1 hour (A + B) fill = (3/7) * (1/10) = (3/70) unit of water.
Therefore,
→ C will fill per hour = (A + B + C) - (A + B) = (1/7) - (3/70) = (10 - 3)/70 = (7/70) = (1/10) unit .
Hence,
→ C will fill complete cistern in = 10 hours. (Ans.)
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