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CAT Previous Year Paper | CAT Pipes and Cisterns Questions | Question 21

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Question 21 : A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump A or pump B or both start working until the tank is full. On Monday, A alone completed filling the tank at 8 pm. On Tuesday, B alone completed filling the tank at 6 pm. On Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank. At what time was the tank filled on Thursday if both pumps were used simultaneously all along?

  1. 4 : 12 PM
  2. 4 : 24 PM
  3. 4 : 48 PM
  4. 4 : 36 PM

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Explanatory Answer

Method of solving this CAT Question from Pipes and Cisterns
CAT 2018 Question Paper Quants Slot 2 Pipes and Cisterns

Given that a tank is emptied everyday at a fixed time point and after that either pump A or B or both start working to fill the tank.
On Monday, A alone completed filling the tank at 8 pm.
On Tuesday, B alone completed filling the tank at 6 pm.
On Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank.
We have to find at what time will the tank filled on thursday if both were used simultaneously all along

A is doing 3 hours less work on Wednesday which B completes in 2 hours therefore B = 1.5 A
⟹ \\frac{n}{n - 2}) = \\frac{3}{2})
⟹ 2n = 3n – 6
⟹ n = 6
A takes 6 hours and B takes 4 hours or the tank is closed at 2 pm
When they are together open
⟹ \\frac{1}{6}) + \\frac{1}{4}) = \\frac{2 + 3}{12})
⟹ Rate is \\frac{5}{12}) or they can fill the entire tank in \\frac{12}{5}) hours which is 2 hours 24 minutes
Starting from 2 pm, they fill the entire tank by 4:24 pm
Here the break through is figuring out the ratio or efficiency of the rate at which they fill is B : A = 3 : 2
The conventional way is
⟹ \\frac{n - 3}{n}) + \\frac{2}{n - 2}) = 1
n-3 hours at the rate of \\frac{1}{n}) per hour
2 hours at the rate \\frac{1}{n - 2}) per hour
Solving this we get n = 6 and we can find solution using this n.

The question is "A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump A or pump B or both start working until the tank is full. On Monday, A alone completed filling the tank at 8 pm. On Tuesday, B alone completed filling the tank at 6 pm. On Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank. At what time was the tank filled on Thursday if both pumps were used simultaneously all along?"

Hence, the answer is 4 : 24 PM

Choice B is the correct answer.

 

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