Question 1

A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

Accepted Answer

Suppose pipe A alone takes x hours to fill the tank. Then, pipes B and C will take x and x hours respectively to fill the tank. 2 4 ∴ 1 + 2 + 4 = 1 x x x 5 ⟹ 7 = 1 x 5 ⟹ x = 35 hrs.

Question 2

Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?

Accepted Answer

Let the cistern be filled by pipe A alone in x hours. Then, pipe B will fill it in (x + 6) hours. ∴ 1 + 1 = 1 x (x + 6) 4 ⟹ x + 6 + x = 1 x(x + 6) 4 ⟹ x2 - 2x - 24 = 0 ⟹ (x -6)(x + 4) = 0 ⟹ x = 6. [neglecting the negative value of x]

Question 3

Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is:

Accepted Answer

Part filled in 2 hours = 2 = 1 6 3 Remaining part = ❨ 1 - 1 ❩ = 2 . 3 3 ∴ (A + B)'s 7 hour's work = 2 3 (A + B)'s 1 hour's work = 2 21 ∴ C's 1 hour's work = { (A + B + C)'s 1 hour's work } - { (A + B)'s 1 hour's work } = ❨ 1 - 2 ❩ = 1 6 21 14 ∴ C alone can fill the tank in 14 hours.

Question 4

A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe…

Accepted Answer

Suppose, first pipe alone takes x hours to fill the tank . Then, second and third pipes will take (x -5) and (x - 9) hours respectively to fill the tank. ∴ 1 + 1 = 1 x (x - 5) (x - 9) ⟹ x - 5 + x = 1 x(x - 5) (x - 9) ⟹ (2x - 5)(x - 9) = x(x - 5) ⟹ x2 - 18x + 45 = 0 (x - 15)(x - 3) = 0 ⟹ x = 15. [neglecting x = 3]

Question 5

Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?

Accepted Answer

Part filled by A in 1 min = 1 . 20 Part filled by B in 1 min = 1 . 30 Part filled by (A + B) in 1 min = ❨ 1 + 1 ❩ = 1 . 20 30 12 ∴ Both pipes can fill the tank in 12 minutes.

Question 6

Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in:

Accepted Answer

(A + B)'s 1 hour's work = ❨ 1 + 1 ❩ = 9 = 3 . 12 15 60 20 (A + C)'s hour's work = ❨ 1 + 1 ❩ = 8 = 2 . 12 20 60 15 Part filled in 2 hrs = ❨ 3 + 2 ❩ = 17 . 20 15 60 Part filled in 6 hrs = ❨ 3 x 17 ❩ = 17 . 60 20 Remaining part = ❨ 1 - 17 ❩ = 3 . 20 20 Now, it is the turn of A and B and 3 part is filled by A and B in 1 hour. 20 ∴ Total time taken to fill the tank = (6 + 1) hrs = 7 hrs.

Question 7

Two pipes A and B can fill a cistern in 37½ minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:

Accepted Answer

Let B be turned off after x minutes. Then, Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1. ∴ x ❨ 2 + 1 ❩ + (30 - x). 2 = 1 75 45 75 ⟹ 11x + (60 -2x) = 1 225 75 ⟹ 11x + 180 - 6x = 225. ⟹ x = 9.

Question 8

Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P,Q and R respectively. What is the pro…

Accepted Answer

Part filled by (A + B + C) in 3 minutes = 3 ❨ 1 + 1 + 1 ❩ = ❨ 3 x 11 ❩ = 11 . 30 20 10 60 20 Part filled by C in 3 minutes = 3 . 10 ∴ Required ratio = ❨ 3 x 20 ❩ = 6 . 10 11 11

Question 9

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 - ❨ 1 + 1 ❩ 15 20 24 = ❨ 1 - 11 ❩ 15 120 = - 1 . [-ve sign means emptying] 40 ∴ Volume of 1 part = 3 gallons. 40 Volume of whole = (3 x 40) gallons = 120 gallons.

Question 10

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 four taps in 1 hour = ❨ 4 x 1 ❩ = 2 . 6 3 Remaining part = ❨ 1 - 1 ❩ = 1 . 2 2 ∴ 2 : 1 :: 1 : x 3 2 ⟹ x = ❨ 1 x 1 x 3 ❩ = 3 hours i.e., 45 mins. 2 2 4 So, total time taken = 3 hrs. 45 mins.

Question 11

Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:

Accepted Answer

Net part filled in 1 hour ❨ 1 + 1 - 1 ❩ = 17 . 5 6 12 60 ∴ The tank will be full in 60 hours i.e., 3 9 hours. 17 17

Question 12

A pump can fill a tank with water in 2 hours. Because of a leak, it took 2⅓ hours to fill the tank. The leak can drain all the water of the tank in:

Accepted Answer

Work done by the leak in 1 hour = ❨ 1 - 3 ❩ = 1 . 2 7 14 ∴ Leak will empty the tank in 14 hrs.

Question 13

Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?

Accepted Answer

Part filled in 4 minutes = 4 ❨ 1 + 1 ❩ = 7 . 15 20 15 Remaining part = ❨ 1 - 7 ❩ = 8 . 15 15 Part filled by B in 1 minute = 1 20 ∴ 1 : 8 :: 1 : x 20 15 x = ❨ 8 x 1 x 20 ❩ = 10 2 min = 10 min. 40 sec. 15 3 ∴ The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec.

Question 14

A large tanker can be filled by two pipes A and B in 60 minutes 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 + 1 ❩ = 1 . 60 40 24 Suppose the tank is filled in x minutes. Then, x ❨ 1 + 1 ❩ = 1 2 24 40 ⟹ x x 1 = 1 2 15 ⟹ x = 30 min.

Question 15

One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe 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 minutes. 3 ∴ 1 + 3 = 1 x x 36 ⟹ 4 = 1 x 36 ⟹ x = 144 min.

Question 16

Pipe A can fill a tank in 45 hrs and pipe B can fill it in 36 hrs. If both the pipes are opened in the empty tank. In how many hours will it be full?

Accepted Answer

Part filled A in 1 hr= (1/45) Part filled B in 1 hr= (1/36) Part filled by (A+B) together in 1 hr=(1/45)+(1/36)=1/20 So, The tank will be full in 20 hr.

Question 17

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 1h = 1/6 part

Question 18

A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?

Accepted Answer

Work done by leak in 1 hour = (1/8 - 1/10) = 1/40 ∴ The leak will empty the cistern in 40 hours.

Question 19

A pipe can empty a tank in 12 minutes and another pipe can empty it in 16 minutes. If both the pipes are opened simultaneously, find the time in which a full tank is emptied?

Accepted Answer

Required answer = (12 x 16) /(12 + 16) = 48 / 7 = 66/7 minutes.

Question 20

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

Accepted Answer

Here x = 8 hrs. and y = 8 + 2 = 10 hrs. Now, applying the given rule, we have the Required answer = (8 x 10) /(10 - 8) = 40 hrs.

Pipes and Cistern Questions