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Inlet Pipe A can fill can cistern is 35 hours while outlet Pipe B can drain the filled cistern in 40 hours. The two pipes are opened together when the cistern is empty, but the outlet pipe is closed when the cistern is three-fifths full. How many hours did it take in all to fill the cistern?

Inlet Pipe A can fill can cistern is 35 hours while outlet Pipe B can drain the filled cistern in 40 hours. The two pipes are opened together when the cistern is empty, but the outlet pipe is closed when the cistern is three-fifths full. How many hours did it take in all to fill the cistern? Correct Answer 182

Given,

Inlet Pipe A can fill can cistern is 35 hours,

Therefore, A fill the tank in 1 hour = 1/35

B empty the tank in 1 hour = 1/40

A and B can fill the tank in 1 hour = (1/35) – (1/40) = 1/280

Let the two pipes are opened together for X hour till the cistern is three-fifths full

Therefore,

A and B together can fill the tank in X hour = X/280

⇒ X/280 = 3/5

⇒ X = 168 hour.

Now according to the question,

The outlet pipe is closed when the cistern is three-fifths full.

Therefore, remaining part (1 – 3/5) = 2/5 of the tank will be filled by the inlet pipe A,

Time taken by the inlet pipe to fill the remaining tank = (2/5)/ (1/35) = (2/5) × 35 = 14 hour.

Therefore, the total time to fill the tank = (168 + 14) = 182 hours.

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