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There is a leakage at the bottom of the tank which can empty the tank in 60 hours. Pipe A can fill the tank in 10 hours while pipe B can empty the tank in 40 hours. If pipe A alone opened till 3/4th tank gets filled and then pipe B is opened. In how many hours tank gets completely filled?

There is a leakage at the bottom of the tank which can empty the tank in 60 hours. Pipe A can fill the tank in 10 hours while pipe B can empty the tank in 40 hours. If pipe A alone opened till 3/4th tank gets filled and then pipe B is opened. In how many hours tank gets completely filled? Correct Answer 93/7 hours

Given:

Pipe A can fill the tank in 10 hours

Leakage can empty the tank in 60 hours

Pipe B can empty the tank in 40 hours

Calculation:

Pipe A can fill the tank in 10 hours

⇒ Pipe A's 1 hour’s work = 1/10

Pipe B can empty the tank in 40 hours

⇒ Pipe B's 1 hour's work = 1/40

Leakage can empty the tank in 60 hours

⇒ Leakage 1 hour's work = 1/60

⇒ Pipe A and leakage 1 hour's work = 1/10 – 1/60 = 1/12 units

Time taken by Pipe A and leakage to fill 3/4th of tank = 3/4 × 12

⇒ 9 hours

Now,

Pipe B is also opened

Pipe A, leakage and pipe B’s 1 hour work = 1/10 – 1/60 – 1/40 = 7/120

⇒ Time is taken by all three to fill 1/4th of tank = 1/4 × 120/7 = 30/7 hours

∴ Total time required to fill the tank = 9 + 30/7 = 93/7 hours.

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