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When operated separately, pipe A takes 5 hours less than pipe B to fill a cistern, and when both pipes are operated together, the cistern gets filled in 6 hours. In how much time (in hours) will pipe B fill the cistern, if operated separately?

When operated separately, pipe A takes 5 hours less than pipe B to fill a cistern, and when both pipes are operated together, the cistern gets filled in 6 hours. In how much time (in hours) will pipe B fill the cistern, if operated separately? Correct Answer 15

Given:

Pipe A takes 5 hours less than pipe B to fill a cistern.

Time to fill the tank by pipe A and B together = 6 hours

Formula used:

Efficiency = Total work/total time

Concept used:

Let time to fill the whole tank by pipe B alone be x hours.

So, time to fill the whole tank by pipe A will be (x - 5) hours.

Let capacity of total tank be 6x(x - 5) units.

Efficiency of pipe A = 6x(x - 5)/(x - 5)

⇒ 6x units/hour

Efficiency of pipe B = 6x(x - 5)/x

⇒ 6(x - 5) units/hour

Efficiency of A and B together = 6x(x - 5)/6

⇒ x(x - 5) units/hour

Equating combined efficiency,

6x + 6(x - 5) = x(x - 5)

⇒ 6x + 6x - 30 = x2 - 5x

⇒ 12x - 30 = x2 - 5x

⇒ x2 - 5x - 12x + 30 = 0

⇒ x2 - 17x + 30 = 0

⇒ (x - 15)(x - 2) = 0

Taking (x - 15) = 0

⇒ x = 15 hours

∴ Pipe B will fill the cistern in 15 hours.

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