Pipe & Cistern Quiz

1 >>Q1.Pipe 'A' can fill A tank in 20 minutes. Pipe'A' and 'B' both are opened and after 6 minutes pipe 'A' is closed and pipe 'B' takes 15 minutes to fill the tank. In how many minutes, can pipe 'B' fill the tank? ?

• (A) 33
• (B) 30
• (C) 28
• (D) 35

Solution Exp. Let pipe 'B' fill X parts of a tank in a minute.Pipe 'A' fills 1/20 th of a tank in one minute.In 6 minutes, 6/20 + 6X parts of tank is filled.In next 15 minutes, 15X parts of tank is filled.6/20 + 6X + 15X = 1 (full tank).X = 1/30.Pipe 'B' takes 30 minutes to fill the tank (1/(1/30)).

2 >>Q2. Pipe 'A' can fill 12 litres per minute and pipe 'B' can fill 6 litres per minute. Pipe 'C' can empty a drum in 10 minutes. When all the three pipes are opened, the drum is filled in 15 minutes. What is the capacity of drum? ?

• (A) 114 litres
• (B) 110 litres
• (C) 108 litres
• (D) 105 litres

Solution Exp. In 15 minutes, amount of litres filled = 12x15 + 6x15 = 270 litres.Amount removed = 1.5 drums.Remaining amount = 1drum.270litres - 1.5drums = 1drum.1drum = 108 litres.

3 >>Q3. Pipe 'A' can fill a tank in 40 minutes and pipe 'B' can empty the tank 50 minutes. If both the pipes are opened together, then in what time is the tank filled? ?

• (A) 120 min
• (B) 150 min
• (C) 200 min
• (D) 170 min

Solution Exp. Pipe 'A' fills 1/40th of tank in a minute.Pipe 'B' empties 1/50th of tank in a minute.Let X be time taken to fill the tank.X/40 - X/50 = 1 (full tank).X = 200.

4 >>Q4. Pipe 'A' can fill an empty tank in 3 hours less than the time in which pipe 'B', can empty a full tank. If both the pipes are opened together, the tank is filled in 60 hours. In how many hours can pipe 'A' fill the tank? ?

• (A) 24 hours
• (B) 15 hours
• (C) 18 hours
• (D) 12 hours

Solution Exp. Let Pipe 'A' take X hours to fill the tank.Pipe 'B' takes (X+3) hours to empty the tank.60/X - 60/(X+3) = 1 (full tank).X = 12 hours.

5 >>Q5. Pipe 'A' can fill a tank in 18 minutes. Pipe 'A' and 'B' can together fill the tank in 12 minutes. What is the capacity (in litres) of the tank, given that pipe 'B' can fill 15 litres per minute? ?

• (A) 540 litres
• (B) 480 litres
• (C) 270 litres
• (D) 350 litres

Solution Exp. Let pipe 'B' take X minutes to fill the tank.In 12 minutes, pipe 'A' fills 12/18th of tank and pipe 'B' fills 12/X th of the tank.Since tank is full, 12/18 + 12/X = 1.X = 36.Pipe 'B' takes 36 minutes to fill the tank.It fills 15 litres per minute, hence capacity of tank = 36x15 = 540 litres.

6 >>Q6. Two pipes can fill a tank in 15 minutes and 25 minutes respectively. Both pipes are opened together and after some time the first pipe is closed and the tank is full in totally 15 minutes. For how many minutes was first pipe open? ?

• (A) 7
• (B) 8
• (C) 6
• (D) 9

Solution Exp. Let first pipe be open for X minutes.Amount of tank filled in X minutes = X/15 + X/25.Amount of tank filled in remaining time (only by 2nd pipe) = (15-X)/25.X/15 + X/25 + (15-X)/25 = 1.X/15 + X/25 + 3/5 - X/25 = 1.X = 6.

7 >>Q7. Pipe 'A' can fill a tank in 8 hours and pipe 'B' can empty the full tank in 15 hours. If the both pipes are opened together, in how much time will the tank become full? ?

• (A) 15
• (B) 14
• (C) 17
• (D) 16

Solution Exp. Let X(in hours) be the time taken to fill the tank.X/8 - X/15 = 1.X = 17.

8 >>Q8. Two pipes 'A' and 'B' can fill a tank in 24 minutes and 32 minutes respectively. Both the pipes are opened together, but after 4 minutes the second pipe is turned off. In how much time will the tank be completely filled by the first pipe? ?

• (A) 18 minutes
• (B) 16 minutes
• (C) 17 minutes
• (D) 15 minutes

Solution Exp. Amount of tank filled in 4 minutes by both A and B = 4/24 + 4/32 = 7/24.Amount to be filled by A alone = 1 - 7/24 = 17/24.A can fill 1/24th of the tank in one minute.Hence it requires 17 minutes to fill 17/24 th of the tank.

9 >>Q9. Pipe 'A' can fill a cistern in 30 minutes and pipe 'B' in 40 minutes and pipe 'C' can empty the full cistern in 60 minutes. If all the pipes are opened together, then in how many minutes will it be full ? ?

• (A) 25
• (B) 26
• (C) 24
• (D) 27

Solution Exp. Let X be the time taken for the tank to be full.X/30 + X/40 - X/60 = 1.X = 24.

10 >>Q12. If two pipes P and Q together can fill a tank in 6 hours and the pipe P only can fill the tank in 8 hours, how many hours will Q alone take to fill the tank? ?

• (A) 24 hours
• (B) 21 hours
• (C) 18 hours
• (D) 10 hours

Solution Exp. Let X be the time taken by pipe Q to fill the tank.The two pipes together fill the tank in 6 hours.6/8 + 6/X = 1.X = 24.

11 >>Q14. Two pipes can fill a cistem in 8 hours and 10 hours respectively. A third pipe can empty the cistern in 5 hours. If all the three pipes are opened at the same time, how long will it take to fill the cistern? ?

• (A) 15 hours
• (B) 16 hours
• (C) 12 hours
• (D) 11 hours

Solution Exp. Let X be the time taken to fill the cistern.X/8 + X/10 - X/5 = 1.X = 16.

12 >>Q15. Two taps can fill a cistern in 2 and 4 hours respectively. How much time after opening the both taps, second tap should be turned off so that the cistern be filled in 1 hour? ?

• (A) 1/3 hours
• (B) 1 hour
• (C) 2/3 hours
• (D) 2 hours

Solution Exp. Let X be the time both taps operate.Amount of cistern filled in X hours = X/2 + X/4.Amount of cistern filled in the next hour = 1/2.X/2 + X/4 + 1/2 = 1.X = 2/3.

13 >>Q16. Two taps can fill a cistern in 6 minutes and 7 minutes respectively. If these taps are opened alternately for a minute, in what time will the cistern be filled? ?

• (A) 7 3/7 min.
• (B) 2 3/7 min.
• (C) 3 3/7 min.
• (D) 6 3/7 min.

Solution Exp. Amount filled in two minutes = 1/6 + 1/7 = 13/42.After 6 minutes, amount filled = 39/42.Now first tap is opened, it fills 1/6 th of cistern in one minute.To fill 3/42 th of a cistern, it should be open for (3/42)/(1/6) = 3/7minutes.Total time = 6 3/7 minutes.

14 >>Q17. A cistern can be filled by one of two pipes in 30 min. and by the other in 36 min. Both pipes are opened together for a certain time but being particularly clogged only 5/6 of the full quantity of water flows through the former and only 9/10 through the later. The obstructions, howevers, being suddenly removed the cistern is filled in 15 1/2 min. from that moment. How long was it before the full flow of water began? ?

• (A) 1/7 min.
• (B) 1/3 min.
• (C) 1/2 min.
• (D) 1 min.

Solution Exp. Let X be the time the pipes were blocked.Amount of cistern filled = (5/6)(X/30) + (9/10)(X/36) = 19X/360.Amount of cistern filled after removal of clogging = (15.5)/30 + (15.5)/36.19X/360 + 15.5/30 + 15.5/36 = 1.X = 1.

15 >>Q18. P, Q, R are pipes attached to a cistern, P and Q can fill it in 20 and 30 min. respectively. While R can empty it in 15 min. If P, Q and R be kept open successively for 1 min. each, how soon will the cistern be filled? ?

• (A) 157 min.
• (B) 167 min.
• (C) 165 min.
• (D) 164 min.

Solution Exp. Amount of cistern filled in 3 minutes = 1/20 + 1/30 - 1/15 = 1/60.In 165 minutes (3x55), amount of cistern filled = 55/60.In the next minute, amount of cistern filled = 55/60 + 1/20 = 58/60.In the next minute, amount of cistern filled = 58/60 + 1/300 = 1.Hence it takes 167 minutes (165+1+1).Q20. A cistern which could be filled in 9 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full, in what time will the leak empty it? 90 hours 96 hours 100 hours 119 hoursAns.AExp. Let X be the time taken by the leakage to empty the cistern when it is full.Amount of time taken to fill cistern = 10 hours.10/9 - 10/X = 1.X = 90.