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1. Two pipe A and B can fill a water tank in 20 and 24 minutes respectively and a third pipe C can empty at the rate of 3 gallons per minute. If A, B and C are open together to fill the tank in 15 minutes, find the capacity of tank?

A. 180 gallons

B. 150 gallons

C. 120 gallons

D. 60 gallons

Solution:

Work done by the C pipe in 1 minute

\begin{aligned} = \frac{1}{15} - (\frac{1}{20} + \frac{1}{24}) \\ = (\frac{1}{15} - \frac{11}{120}) \\ = - \frac{1}{40} [- ve means emptying] \end{aligned}

∴ Volume of

\frac{1}{40}

part = 3 gallons.
Volume of whole = (3 × 40) gallons = 120 gallons.

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