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GATE 2022 XH5 (Psychology) – Question 3

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 1 mark · Multiple choice

Pipes P and Q can fill a storage tank in full with water in 10 and 6 minutes, respectively. Pipe R draws the water out from the storage tank at a rate of 34 litres per minute. P, Q and R operate at a constant rate.

If it takes one hour to completely empty a full storage tank with all the pipes operating simultaneously, what is the capacity of the storage tank (in litres)?

  1. 26.8
  2. 60.0
  3. 120.0
  4. 127.5

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Correct answer: (C) 120.0

Explanation

Let the capacity be $C$ litres. P and Q together fill $C\left(\frac{1}{10} + \frac{1}{6}\right) = \frac{4C}{15}$ litres per minute, while R removes 34. The tank loses $C/60$ per minute, so $34 - \frac{4C}{15} = \frac{C}{60}$, which gives $34 = \frac{17C}{60}$ and $C = 120$.