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CAT 2018 Question Paper | Quants Slot 2

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

This wonderful question is based on Work and Time. Previously, there have been at least one or two questions based on this topic in the CAT Exam as seen in 2IIM's CAT Blueprint. Solve this work and time question and ace your way through the CAT Question Paper

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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