CAT 2023 Slot 2 QA Q10 Time & Work

Question 10 of the Quantitative Ability (QA) section, CAT 2023 Slot 2, with CAT's official answer and a worked solution.

Pipes A and C are fill pipes while Pipe B is a drain pipe of a tank. Pipe B empties the full tank in one hour less than the time taken by Pipe A to fill the empty tank. When pipes A, B and C are turned on together, the empty tank is filled in two hours. If pipes B and C are turned on together when the tank is empty and Pipe B is turned off after one hour, then Pipe C takes another one hour and 15 minutes to fill the remaining tank. If Pipe A can fill the empty tank in less than five hours, then the time taken, in minutes, by Pipe C to fill the empty tank is
  1. A
    90
  2. B
    60
  3. C
    120
  4. D
    75

Answer: (A) 90 Time & Work MCQ

Solution

  1. Let A fill in \(a\) hours, B empty in \(a-1\) hours, C fill in \(c\) hours. All three together: \(\frac1a - \frac1{a-1} + \frac1c = \frac12\).
  2. B and C for 1 hour, then C alone for 1.25 hours fills the tank: \(\frac{2.25}{c} - \frac{1}{a-1} = 1\).
  3. Substitute \(\frac1c = \frac12 - \frac1a + \frac1{a-1}\): \(1.125 - \frac{2.25}{a} + \frac{1.25}{a-1} = 1\), i.e. \(\frac{18}{a} - \frac{10}{a-1} = 1\), so \(a^2 - 9a + 18 = 0\) and \(a = 3\) or \(6\).
  4. Since \(a < 5\), \(a = 3\). Then \(\frac1c = \frac12 - \frac13 + \frac12 = \frac23\), so \(c = 1.5\) hours \(= 90\) minutes.

Same concept in other years

See every question on Pipes and cisterns with a draining pipe: net rate = fill − drain.

More Time & Work questions from CAT

All 34 Time & Work questions asked since 2017.