← Quantitative Aptitude

Time & Work (Pipes) — Questions with Solutions

4 solved Time & Work (Pipes) questions from Quantitative Aptitude, as asked in SSC CGL and other SSC exams. Read the answer and explanation below, then practise the full set in the practice section.

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Q1. Pipes P, Q and R can fill a cistern in 40, 80 and 120 minutes. All are opened. After how much time should Q and R be turned off so the cistern is filled in just half an hour?

पाइप P, Q और R एक टंकी को 40, 80 और 120 मिनट में भर सकते हैं। सभी खोले गए हैं। Q और R को कितने समय बाद बंद कर देना चाहिए ताकि टंकी ठीक आधे घंटे (30 मिनट) में भर जाए?

  1. A. $14\text{ mins}$
  2. B. $10\text{ mins}$
  3. C. $16\text{ mins}$
  4. D. $12\text{ mins}$

Solution

Total capacity = $240$. Efficiency: P=6, Q=3, R=2. P operates for 30 mins, filling $30 \times 6 = 180$ units. Remaining 60 units must be filled by Q+R. Time for Q+R = $\frac{60}{3+2} = 12\text{ mins}$.

Q2. Fill pipe P is 21 times faster than fill pipe Q. If Q can fill a cistern in 110 minutes, find the time it takes to fill the cistern when both fill pipes are opened together.

  1. A. 5 minutes
  2. B. 4 minutes
  3. C. 3 minutes
  4. D. 6 minutes

Solution

Let efficiency of Q = 1, then P = 21. Total capacity = 110 * 1 = 110 units. Time taken together = 110 / (21 + 1) = 110 / 22 = 5 minutes.

Q3. A pipe can fill an overhead tank in $12\text{ hours}$. But due to a leak at the bottom, it is filled in $18\text{ hours}$. If the tank is full, how much time will the leak take to empty it?

एक पाइप एक ओवरहेड टैंक को $12\text{ घंटे}$ में भर सकता है। लेकिन तल में रिसाव के कारण यह $18\text{ घंटे}$ में भरता है। यदि टैंक भरा हुआ है, तो रिसाव इसे खाली करने में कितना समय लेगा?

  1. A. $3.6\text{ hours}$
  2. B. $63\text{ hours}$
  3. C. $7.2\text{ hours}$
  4. D. $36\text{ hours}$

Solution

Let leak empty in $x$ hours. $1/12 - 1/x = 1/18 \implies 1/x = 1/12 - 1/18 = 1/36$. So, leak takes $36\text{ hours}$.

Q4. Pipes M, N and S can fill a tank in 25, 50 and 100 minutes, respectively. Initially, pipes N and S are kept open for 10 minutes, and then pipe N is shut while pipe M is opened. Pipe S is closed 15 minutes before the tank overflows. How much time (in minutes) will it take to fill the tank if the three pipes work in this pattern?

  1. A. 30
  2. B. 33
  3. C. 42
  4. D. 27

Solution

Total capacity = LCM(25,50,100) = 100. Efficiencies: M=4, N=2, S=1. First 10 mins (N+S): (2+1)*10 = 30 units. Remaining = 70. Last 15 mins (only M works as S is closed): 4 * 15 = 60 units. The middle phase (M+S) fills the rest: 70 - 60 = 10 units. Time for middle phase = 10 / (4+1) = 2 mins. Total time = 10 + 2 + 15 = 27 mins.