DI on Pipe and Cistern

Data Interpretation (DI) is one of the most important topics in the Quantitative Aptitude section of various bank exams in the year 2020-21. Usually, candidates take a lot of time to solve these type of questions in bank exams.

In this study Note we will discuss  DI based on Pipe and Cistern

Direction (1-5): Study the following table to answer the questions that follow. Some values are missing. Study the table carefully and answer the questions based on data in table and particular questions.

Question 1: To fill a tank, pipes A and C were opened at 2:10 PM . After 5 minutes pipe A was closed and at the same time pipe P got opened. After some time it was found that tank was 2/3rd empty, at what time it was observed ?
A) 2:32 PM             B) 2:30 PM                   C) 2:27 PM                    D) 2:35 PM                  E) 2:20 PM

Solution:
A and C work for 5 minutes – (1/15 + 1/25) * 5 = 8/15 tank fill
Now A was closed and C and P work

In 1 minute they work = (1/25 – 1/20) = -1/100 — means empty
let they C and P work for x minutes up to when tank was found 2/3rd empty
So
8/15 + (-1/100)*x = 1/3        ….   [ 1/3rd tank is fill at this time]
Solve,  x = 20 mins
So the time when 2/3rd empty tank was observed – 2:10 + 5 minutes + 20 minutes = 2:35 PM

Hence option C is correct.

Question 2: A tank was 2/5th full. To fill it more, pipe D was to be opened, but accidentally pipe Q got opened. When it was noticed after 4 minutes, pipe Q was closed. And now to fill tank quickly, pipe C was opened. What time could have been saved if pipe Q was not opened ?
A) 7.45 minutes       B) 5.35 minutes        C) 5.25 minutes         D) 8.35 minutes        E) 7.25 minutes  
Solution:
Tank was 2/5th full. So to fill 3/5th tank, D will take 3/5 * 30 = 18 minutes …………………….(1)
Now
Pipe Q was opened for 4 minutes, so it emptied = 1/16 * 4 = 1/4th tank
Now tank filled is = 2/5 – 1/4 = 3/20
Now pipe C was opened, to fill 17/20th tank, C takes = 17/20 * 25 = 85/4  = 21.25 minutes
So total time now taken to fill tank = 4 + 21.25 = 25.25 minutes  ……………………..(2)
So time that could have been saved = 25.25 – 18 = 7.25 minutes  

Hence option E is correct.

Question 3: There was some garbage in a tank. To remove the garbage, pipes A and R worked alternately for 3 minutes each starting with A. The procedure continued for 24 minutes, after which pipes A and D were opened to fill the tank. If the tank was filled in next 7 minutes, find the time in which pipe R can empty the full tank.
A) 24 minutes              B) 28 minutes              C) 18 minutes                D) 20 minutes                    E) 32 minutes
Solution:
Procedure continued for 24 minutes, so pipes A and R both worked for 12 minutes each, giving 3 minutes each in turn.
So in 12 minutes, pipe A’s work = 1/15 *12 = 4/5
In 12 minutes, pipe R’s work = 1/x *12 = 12/x       [Let x = time in which pipe R can empty the tank]
Now A and D worked for 7 minutes, so their work in 7 minutes = (1/15 + 1/30) * 7 = 7/10
So 
4/5 – 12/x + 7/10 = 1
Solve, x = 24 minutes
Hence option A is correct.

Question 4:A tank is to be filled by using pipes B and D simultaneously. After 9 minutes, some garbage was observed in tank so pipes B and D were closed and pipe S was opened. After 6 minutes, it was found, that tank is clean so pipe S was closed and again pipes B and D were opened, after which they filled the tank in 6 minutes. If pipe S alone can empty 2/9th tank in 4 minutes, in how much time pipe B can fill the fill tank?
A) 20 minutes                B) 16 minutes               C) 15 minutes                 D) 24 minutes               E) 18 minutes

Solution:
S can empty 2/9th tank in 4 minutes, so full tank in 9/2 * 4 = 18 minutes
So now
(1/B + 1/30) * 9 + (-1/18) *6 + (1/B + 1/30) * 6 = 1
(1/B + 1/30) * 15 = 1 + 1/3
(1/B + 1/30) * 15 = 4/3
Solve, B = 18

Hence option E is correct.
 

Question 10:Using the data from table and above questions, which of the following combination of pipes will fill the tank in less time as compared to other combinations given ?

A) A-B-S                B) B-C-P                  C) A-D-Q              D) A-B-P                     E) B-D-R
Solution:
A) A-B-S 
[1/15 + 1/18 – 1/18] — 1/15 so this combination will fill tank in 15 minutes 
B) B-C-P
[1/18 + 1/25 – 1/20] — 41/900 so this combination will fill tank in 900/41 = 21.9 minutes
Similarly
C) A-D-Q — 80/3  = 26.6 minutes
D) A-B-P — 180/13  = 13.8 minutes
E) B-D-R — 360/17 = 21.2 minutes

Hence option D is correct.