Question 1

An inlet pipe fills 1/8 part of a tank in 1 h. How much time will the pipe take to fill the empty tank?

Accepted Answer

We know that, when a pipe fills 1/m part of a tank in 1 h, then the pipe takes m h to fill the tank. Here, 1/m = 1/8 ⇒ m = 8 ∴ Required time to fill the tank = 8 h

Question 2

An outlet pipe can empty a cistern in 3 h. In what time will the pipe empty two-third part of the cistern?

Accepted Answer

Time taken by the pipe to empty the cistern = 3 h Then, time taken by the pipe to empty the 2/3 part = 3 x 2/3 = 2 h

Question 3

A pipe can fill a tank in 20 h. Due to a leak in the bottom, it is filled in 40 h. If the tank is full, how much time will the leak take to empty it?

Accepted Answer

Let the leak empties the full tank in x h, then Part emptied in 1 by leak = 1/x Part filled by inlet in 1 h = 1/20 According to the question, 1/20 + 1/x = 1/40 ∴ 1/x = 1/40 - 1/20 = 1- 2/40 = -1/40 [-ve sign Indicates emptying.] Clearly, leak will empty the full tank in 40 h.

Question 4

If a pipe fills a tank in 6 h, then what part of the tank will the pipe fill in 1 h?

Accepted Answer

We know that, when a pipe fills a tank in m h, then the part of tank filled in 1 h = 1/m Here, m = 6 ∴ Required part of the tank to be filled in 1 h = 1/6 part

Question 5

An outlet pipe can empty a cistern in 30 min, then what part of the cistern will it empty in 1 min?

Accepted Answer

We know that, when a pipe empties a cistern in n min, then the part emptied by the pipe in 1 min = 1/n Here, n=30 ∴ Required part of the tank emptied in 1 min = 1/30 part

Question 6

Three pipes A, B and C can fill a tank separately in 8 h,10 h and 20h, respectively. Find the time taken by all the three pipes to fill the tank when these pipes are opened together?

Accepted Answer

Part filled by A in 1 h = 1/8 Part filled by B in 1 h = 1/10 Part filled by C in 1 h = 1/20 Part filled by (A + B + C) in 1 h = 1/8 + 1/10 + 1/20 = (5 + 4 + 2)/40 = 11/40 ∴ Required time to fill the tank = 40/11 h = 37/11 h

Question 7

A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank is already half full and both the taps are opened together, the tank will be?

Accepted Answer

Part emptied in 1 min. = (1/8 - 1/16) = 1/16 ∴ Time taken to empty the full tank = 16 min. Hence, time taken to empty the half tank = 8 min.

Question 8

A cistern can be filled by two pipes A and B in 4 hours and 6 hours respectively. When full, the tank can be emptied by a third pipe C in 8 hours . If all the taps be turned on at the same time, the cistern will be full in?

Accepted Answer

Net filling in 1 hour = (1/4 + 1/6 - 1/8) = 7/24 ∴ Time taken to fill the cistern = (24/7) hrs. = 3 hrs. 26 min.

Question 9

One tap can fill a cistern in 2 hours and another can empty the cistern in 3 hours. How long will they take to fill the cistern if both the taps are opened?

Accepted Answer

Net filling in 1 hour = (1/2 - 1/3) = 1/6 ∴ Time taken to fill the cistern = 6 hours

Question 10

A pipe can fill a tank in x hours and another can empty it in y hours. They can together fill it in (y > x)?

Accepted Answer

Net filling in 1 hour = (1/x - 1/y) = (y - x) / xy ∴ Time taken to fill the tank = xy / (y - x) hrs.

Question 11

A tap can fill a cistern in 8 hours and another can empty it in 16 hours. If both the taps are opened simultaneously, the time (in hours) to fill the tank is?

Accepted Answer

Part filled by intel in 1 hour = 1/8 Part emptied by outlet in 1 hour = 1/16 Net filling in 1 hour = (1/8 - 1/16) = 1/16 ∴ Time taken to fill the tank = 16 hours

Question 12

Pipes A and B can fill a tank in 10 hours and 15 hours respectively. Both together can fill it in?

Accepted Answer

Part filled by A in 1 hour = 1/10 Part filled by B in 1 hours = 1/15 Part filled by (A + B) in 1 hour = (1/10 + 1/15) = 5/30 = 1/6 ∴ Both pipes together can fill the tank in 6 hours.

Question 13

Three are two taps to fill a tank while a third to empty it. When the third tap is closed, they can fill the tank in 10 minutes and 12 minutes respectively. If all the three taps be opened, the tank is filled in 15 minutes. If the first two taps are…

Accepted Answer

Part emptied by the third pipe in 1 min (1/10 + 1/12) - 1/25 = 7/60 So, the full tank will be emptied by third pipe in = (60/7) min. = 8 min. 34 ec.

Question 14

A tap can fill a tank in 25 minutes and another can empty it in 50 minutes. Find whether the tank will be filled up or emptied and in how many minutes?

Accepted Answer

T = (25 x 50) / (50 - 25) = + 50 minutes + ve sign shows that tank is filled up in 50 minutes.

Question 15

Two pipes A and B can fill a tank in 18 and 6 h, respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?

Accepted Answer

Part filled by A in 1 h = 1/18 Part filled by B in by 1 h = 1/6 Part filled (A + B) in 1 h =1/18 + 1/6 = (1 + 3)/18 = 4/18 = 2/9 Hence, both the pipes together will fill the tank in 9/2 h or 41/2 h

Question 16

A cistern can be filled up in 4 h by an inlet A. An outlet B can empty the cistern in 8 h. If both A and B are opened simultaneously, then after how much time will the cistern get filled?

Accepted Answer

Part filled by A in 1 h = 1/4 Part emptied by B in 1 h = 1/8 Part filled by (A + B) In 1 h = 1/4+ ( -1/8 ) = 1/4 - 1/8 = (2 - 1)/8 = 1/8 ∴ Required time to fill the cistern = 8

Question 17

Pipes A and B can fill a tank in 5 and 6 h, respectively. Pipe C can fill it in 30 h. If all the three pipes are opened together, then in how much time the tank will be filled up?

Accepted Answer

Part filled by A in 1 h = 1/5 Part filled by B in 1 h = 1/6 Part filled by C in 1 h = 1/30 Net part filled by ( A + B + C ) in h 1 = ( 1/5 + 1/6 + 1/30 ) = (6 + 5 + 1)/30 = 12/30 = 2/5 ∴ Required time to fill the tank = 5/2 = 21/2 h

Question 18

A tap can fill an empty tank in 12 h and a leakage can empty the tank in 20 h. If tap and leakage both work together, then how long will it take to fill the tank?

Accepted Answer

Part filled by tap in 1 h = 1/12 Part emptied by leak in 1 h = 1/20 Net part filled in 1 h when both (tap and leakage) work = 1/12 - 1/20 = (5 - 3)/60 = 2/60 = 1/30 ∴ Required time to fill the tank = 30 h

Question 19

Three taps A, B and C together can fill an empty cistern in 10 min . The tap A alone can fill it in 30 min and the tap B alone can fill it in 40 min. How long will the tap C alone take to fill it?

Accepted Answer

Part filled by (A + B + C ) in 1 min = 1/10 Part filled by A in 1 min = 1/30 Part filled by B in 1 min = 1/40 Part filled by (A+B) in 1 min = 1/30 + 1/40 = (4 + 3)/120 = 7/120 ∴ Part filled by C in 1 min = 1/10 - 7/120 = (12 - 7)/120 = 5/120 = 1/24 ∴ Tap C will fill the cistern in 24 min.

Question 20

Two pipes A and B can fill a cistern in 15 and 20, respectively. Both the pipes are opened together, but after 2 min, pipe A is turned off. What is the total time required to fill the tank?

Accepted Answer

Part filled by both in 2 min = 2 x ( 1/15 + 1/20 ) = 2 x ( 4 + 3)/60 = 7/30 Part unfilled = 1 - 7/30 = (30 - 7)/30 = 23/30 Now, B fills 1/20 part in 1 min. ∴ 23/30 part will be filled by B in (20 x 23)/30 min or in 46/3 min. ∴ Required time taken to fill the tank = 2 + 46/3 = 52/3 min.

Pipes and Cistern Questions