CAT 2021 Slot 2 · Quant · Question 21

CAT 2021 Slot 2 previous year question on Time and Work, with the answer and a step-by-step solution.

Time and WorkArithmeticMultiple choiceMedium

Two pipes A and B are attached to an empty water tank. Pipe A fills the tank while pipe B drains it. If pipe A is opened at 2 pm and pipe B is opened at 3 pm, then the tank becomes full at 10 pm. Instead, if pipe A is opened at 2 pm and pipe B is opened at 4 pm, then the tank becomes full at 6 pm. If pipe B is not opened at all, then the time, in minutes, taken to fill the tank is

A
140
B
120
C
144
D
264

Pick an option, then check.

Answer & solution

Answer: Option C

Let A fill a tanks per hour and B drain b tanks per hour. Count the hours each pipe runs in the two scenarios.

First: A runs 2 pm to 10 pm, which is 8 hours; B runs 3 pm to 10 pm, which is 7 hours. So 8a-7b=1.

Second: A runs 2 pm to 6 pm, which is 4 hours; B runs 4 pm to 6 pm, which is 2 hours. So 4a-2b=1.

From the second equation a=\frac{1+2b}{4}. Substituting into the first: 2\left( 1+2b \right)-7b=1, so 2-3b=1 and b=\frac{1}{3}.

Then a=\frac{1+\frac{2}{3}}{4}=\frac{5}{12} tanks per hour, so A alone takes \frac{12}{5} hours =144 minutes.

CAT 2021 Slot 2 · Quant · Question 21

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