Question 1

A booster pump can be used for filling as well as for emptying a tank. The capacity of the tank is 2400 m3 . The emptying capacity of the tank is 10 m3 per minute higher than its filling capacity and the pump needs 8 minutes lesser to empty the tank…

Accepted Answer

Let the filling capacity of the pump be x m 3 /min. Then, emptying capacity of the pump=(x+10) m 3 /min. so, 2400 x - 2400 x + 10 = 8 ⇔ x 2 + 10 x - 3000 = 0 ⇒ x - 50 + x + 60 = 0 ⇔ x = 50

Question 2

Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 3 minutes…

Accepted Answer

1/10 + 1/15 = 1/6 x 3 = 1/2 1 - 1/2 = 1/2 1/10 + 1/15 - 1/x = 1/2 x = 8.57 min

Question 3

Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:

Accepted Answer

Work done by the waste pipe in 1 minute = 1 15 - 1 20 + 1 24 = 1 15 - 11 120 = - 1 40 [-ve sign means emptying] Volume of 1 40 part = 3 gallons Volume of whole = (3 x 40) gallons = 120 gallons.

Question 4

There is an empty reservoir whose capacity is 30 litres. There is an inlet pipe which fills at 5 L/min and there is an outlet pipe which empties at 4 L/min. Both the pipes function alternately for 1 minute. Assuming that the inlet pipe is the first …

Accepted Answer

The work to be done = Capacity of reservoir = 30 litres. 1st Minute ---> inlet pipe opened ---> 5 lit filled 2nd minute ---> inlet pipe closed; outlet pipe opened ---> 4 lit emptied In 2 minutes (5 litres - 4 litres = 1lit) is filled into the reservoir. It takes 2 minutes to fill 1lit ---> it takes 50 minutes to fill 25 litres into the reservoir. In the 51st minute inlet pipe is opened and the reservoir is filled.

Question 5

Water flows into a tank which is 200 m long and 150 m wide, through a pipe of cross-section (0.3m x 0.2m) at 20 km/h. In what time will the water level be 12m ?

Accepted Answer

Volume of water collected in the tank in 1 hour ⇒ (0.3 × 0.2 × 20km × 1000mts) = 1200 m cubic If after t hours, the water is at height of 12m, 1200t=200×150×12 ⇒ t = 300 Hours.

Question 6

12 buckets of water fill a tank when the capacity of each tank is 13.5 liters. How many buckets will be needed to fill the same tank,if the capacity of each bucket is 9 liters?

Accepted Answer

Capacity of the tank =(12 x 13.5) liters =162 liters. Capacity of each bucket =9 liters Number of buckets needed = 162/9 =18.

Question 7

One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 min, then the slower alone will be able to fill the tank in:

Accepted Answer

Let the slower pipe alone fill the tank in x minutes. Then,faster pipe will fill it in x/3 minutes. = > 1 x + 3 x = 1 36 = > 4 x = 1 36 = > x = 144 m i n s

Question 8

Two pipes A and B can fill a tank in 16 hrs and 12 hrs respectively. The capacity of the tank is 240 liters. Both the pipes are opened simultaneously and closed after 2 hrs. How much more water need to fill the tank?

Accepted Answer

Given A alone can fill the tank of capacity 240 lit in 16 hrs. => A can fill in 1 hr = 240/16 = 15 lit => B alone can fill the tank of capacity 240 lit in 12 hrs. => B can fill in 1 hr = 240/12 = 20 lit Now, (A + B) in 1 hr = 15 + 20 = 35 lit But they are opened for 2 hrs => 2 x 35 = 70 lit rae filled Remaining water to be filled in tank of 240 lit = 240 - 70 = 170 lit.

Question 9

A large tanker can be filled by two pipes A and B in 60 and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half ?

Accepted Answer

Part filled by (A + B) in 1 minute = (1/60 + 1/40) = 1/24 Suppose the tank is filled in x minutes. Then, x/2(1/24 + 1/40) = 1 (x/2) * (1/15) = 1 => x = 30 min.

Question 10

Pipe A is an inlet pipe that can fill an empty cistern in 69 hours. Pipe B can drain the filled cistern in 46hours. When the cistern was filled the two pipes are opened one at a time for an hour each, starting withPipe B. how long will it take for t…

Accepted Answer

11 days 7 hours

Question 11

Taps X and Y can fill a tank in 30 and 40 minutes respectively.Tap Z can empty the filled tank in 60 minutes.If all the three taps are kept open for one minute each,how much time will the taps take to fill the tank?

Accepted Answer

Given taps X and Y can fill the tank in 30 and 40 minutes respectively. Therefore, part filled by tap X in 1 minute = 1/30 part filled by tap Y in 1 minute = 1/40 Tap Z can empty the tank in 60 minutes. Therefore, part emptied by tap Z in 1 minute = 1/60 Net part filled by Pipes X,Y,Z together in 1 minute = [1/30 +1/40 - 1/60] = 5/120 = 1/24 i.e., the tank can be filled in 24 minutes.

Question 12

The capacity of a tank is 2400 m3 . A pump can be used both for filling and emptying the tank. The emptying capacity of the pump is 10 m3/minute higher than its filling capacity. And also, the pump needs 8 minutes less to empty the tank than to fill…

Accepted Answer

Let filling capacity of the pump be 'F' m 3 / min Then, the filling capacity of the pump will be (F + 10) m 3 / min From the given data, 2400 F - 2400 F + 10 = 8 ⇒ 2400 F + 10 - F F ( F + 10 ) = 8 ⇒ F 2 + 10 F - 3000 = 0 ⇒ F = 50 m 3 / min

Question 13

Pipe A can fill a tank in 16 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes ?

Accepted Answer

Let the pipe B be closed after 'K' minutes. 30/16 - K/24 = 1 => K/24 = 30/16 - 1 = 14/16 => K = 14/16 x 24 = 21 min.

Question 14

The ratio of efficiencies of two filling pipes is 4 : 5. There is a third emptying pipe which efficiency is two third of the average efficiency of first two filling pipes can empty a filled tank in 36 minutes. In how much time both the filling pipes…

Accepted Answer

Let the efficiencies of filling pipes is 4p and 5p respectively. Efficiency of pipe which empty the tank = 2/3 x 9p/2 = 3p Total work = 3p x 36 = 108p Time to fill the tank by both the pipes = 108p/9p = 12 min.

Question 15

A tap can fill a tank in 6 hours. After half the tank is filled three more similar taps are opened. What is the total time taken to fill the tank completely ?

Accepted Answer

Time taken by one tap to fill half of the tank = 3 hrs. Part filled by the taps in 1 hour = 4 x 1/6 = 2/3 Remaining part = 1 - 1/2 = 1/2 2/3 : 1/2 :: 1 : p p = 1/2 x 1 x 3/2 = 3/4 hrs. i.e., 45 min So, total time taken = 3 hrs 45 min.

Question 16

One fill pipe A is 3 times faster than second fill pipe B and takes 32 minutes less than the fill pipe B. When will the cistern be full if both pipes are opened together?

Accepted Answer

Let pipe A takes p min to fill Then, pipe B takes 3p min to fill => 3p - p = 32 => p = 16 min => 3p = 48 min Required, both pipes to fill = (48 x 16)/(48 + 16) min = 12 min.

Question 17

A water tank in a village is normally filled in 8 hours but takes 2 hours longer to fill because of a leak in its bottom. If the tank is full, in how many hrs will the leak empty it ?

Accepted Answer

The time taken by the leak to empty the tank = 1 8 - 1 10 = 5 - 4 40 = 1 40 Therefore, the leak empties the tank in 40 hours.

Question 18

Three taps I, J and K can fill a tank in 20,30and 40 minutes respectively. All the taps are opened simultaneously and after 5 minutes tap A was closed and then after 6 minutes tab B was closed .At the moment a leak developed which can empty the full…

Accepted Answer

Upto first 5 minutes I, J and K will fill => 5[(1/20)+(1/30)+(1/40)] = 65/120 For next 6 minutes, J and K will fill => 6[(1/30)+(1/40)] = 42/120 So tank filled upto first 11 minutes = (65/120) + (42/120) = 107/120 So remaining tank = 13/120 Now at the moment filling with C and leakage @ 1/60 per minute= (1/40) - (1/70) = 3/280. So time taken to fill remaining 13/120 tank =(13/120) /(3/280) = 91/6 minutes Hence total time taken to completely fill the tank = 5 + 6 + 91/6 = 26.16 minutes.

Question 19

A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold ?

Accepted Answer

1/k - 1/20 = -1/24 k = 120 120 x 4 = 480 Therefore, the capacity of the cistern is 480 liters.

Question 20

Two filling taps P and Q together can fill a tank with rate of 40 lit/min and 60 lit/min respectively in 8 min. If a waste tap can empty the filled tank in 32 min, then what is the rate of waste tap ?

Accepted Answer

Given that the waste tap can empty the filled tank in 32 min. Now, the rate at which the waste tap can empty the tank = (40 + 60)8/32 = 100/4 = 25 lit/min.

Pipes and Cistern Questions