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# CAT 2018 Question Paper | Quants Slot 2

###### 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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##### Method of solving this CAT Question from 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. ###### Signup and sample 9 full classes for free The Best Online CAT Coaching Courses. Signup ! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2020Enroll at 44,000/- Next Weekend Batch Starts Sun, Feb 23rd, 2020 ###### Best CAT Coaching in ChennaiRegister Online, get Rs 4000/- off Attend a Demo Class ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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