Bissoy.com
Doctors Medicines MCQs Q&A

An inlet pipe and an outlet pipe are taking to fill and drain a cistern, respectively, for an hour each at a time, starting with the inlet pipe when the cistern is empty. It takes the inlet pipe 15 hours to fully fill the empty cistern, whereas the outlet pipe can drain the filled cistern completely in 21 hours. How many hours will it take for the cistern to be full?

An inlet pipe and an outlet pipe are taking to fill and drain a cistern, respectively, for an hour each at a time, starting with the inlet pipe when the cistern is empty. It takes the inlet pipe 15 hours to fully fill the empty cistern, whereas the outlet pipe can drain the filled cistern completely in 21 hours. How many hours will it take for the cistern to be full? Correct Answer 99

Calculation:

Inlet pipe can fill a cistern in = 15 hours

∴ In 1 hour the inlet pipe can fill = 1/15

Outlet pipe can empty a cistern in = 21 hours

∴ In 1 hour the outlet pipe can empty = 1/21

In 1st our cistern is filled = 1/159

In the next every 2 hours cistern is filled = (1/15 - 1/21) = 2/105

Let, the cistern will be filled in next 2x hours

According to the question,

⇒ 1/15 + 2x/105 = 1

⇒ 2x/105 = 1 - 1/15

⇒ 2x = 14/15 × 105

⇒ 2x = 98

∴ It will take (1 + 98) = 99 hours to fill the cistern

⇒ 98 hours

Total required time = (98 + 1) = 99 hours

∴ It will take 99 hours to make the cistern full.

Related Questions

A pipe, working at full speed, can fill an empty cistern in 1 hour. However, during the first hour it worked at one-twenty-fourth of its capacity, during the second hour at one-twelfth of its capacity, during the third hour at one-eighth of its usual capacity, during the fourth hours at one-fourth of its usual capacity and during the fifth hour it was only one-half as efficient as it was supposed to be. A second pipe also displayed similar performance, but if it worked at full speed would have filled the empty cistern in 2 hours. Together with a drain pipe that drained water out of the tank a constant rate, the empty cistern could be filled in 5 hours, all the three pipe working concurrently. How many hours will it take the drain pipe to empty the filled cistern if no other pipe was functioning during the time?
A pipe, working at full speed, can fill an empty cistern in 1 hour. However, during the first hour it worked at one-twelfth of its capacity, during the second hour at one-ninth of its capacity, during the third hour at one-sixth of its usual capacity and during the fifth hour it was only one -third as efficient as it was supposed to be. A second pipe also displayed similar performance, but if it worked at full speed would have filled the empty cistern in 2 hours. Together with a drain pipe that drained water out of the tank at a constant rate, the empty cistern could be filled in 5 hours, all the three pipes working concurrently. How many hours will it take the drain pipe to empty the filled cistern if no other pipe was functioning during the time?
Two inlet pipes A and B can fill an empty cistern in 35 hours and 52.5 hours respectively while Pipe C is an outlet pipe that can drain the filled cistern in 17.5 hours. When the cistern is full Pipe C is left open for an hour, then closed and Pipe A is opened for an hour, closed and Pipe B is opened for an hour. The process continues till the cistern is empty. How many hours will it take for the filled cistern to be emptied?
Two inlet pipes A & B can fill an empty cistern in 12 hours & 36 hours respectively while Pipe C is an outlet pipe that can drain the filled cistern in 6 hours. When the cistern is full Pipe C is left open for an hour, then closed & Pipe A is opened for an hour, closed and Pipe B is opened for an hour. The process continues till the cistern is empty. How many hours will it take for the filled cistern to be emptied?
A cistern is fitted with many inlets and outlet taps. All inlet taps fill the cistern at the same rate and outlet taps empty the cistern at the same rate. The empty cistern gets filled in 10 hours when 9 inlet and 5 outlet taps are opened. It takes 30 hours when 6 inlets and 5 outlets are opened. How much time does it take for the empty cistern to completely get filled if 2 inlets and 2 outlet taps are opened?
In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: Pipe A takes thrice the time taken by Pipe B to fill a tank. Together they can fill the tank in 15 hours, tank A and B is opened together for 4 hours and then Pipe A is closed and after 2 more hours Pipe B is closed and an outlet Pipe C is opened which when working alone can empty the tank in 10 hours. Calculate the time taken by C to empty the tank. Quantity B: A pipe A can fill the tank in 10 hours another pipe B can fill the tank in 15 hours and with the help of third pipe C they can fill the tank in 5 hours. Pipe A is opened for 4 hours then it is closed, pipe B is closed 3 hours before filling of tank and tank C is opened the whole time. Calculate the time taken to fill the tank
In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: Pipe A takes thrice the time taken by Pipe B to fill a tank. Together they can fill the tank in 15 hours, tank A and B is opened together for 4 hours and then Pipe A is closed and after 2 more hours Pipe B is closed and an outlet Pipe C is opened which when working alone can empty the tank in 10 hours. Calculate the time taken by C to empty the tank. Quantity B: A pipe A can fill the tank in 10 hours another pipe B can fill the tank in 15 hours and with the help of third pipe C they can fill the tank in 5 hours. Pipe A is opened for 4 hours then it is closed, pipe B is closed 3 hours before filling of tank and tank C is opened the whole time. Calculate the time taken to fill the tank.
A tank has an optional adjustable outlet pipe that can be attached to the tank at any height we want. This outlet pipe drains water from the tank at a constant rate, while the tank is being filled using another inlet pipe at a constant rate. If the outlet, pipe is attached at half the height of the tank, the tank, which is initially empty gets filled in 18 hours. If the outlet pipe is attached at height equal to two third height of the tank, the tank, which is initially empty, is filled in 16 hours. In how many hours will the tank, which is initially empty, be completely filled if the outlet pipe is not attached to the tank?
Inlet Pipe A can fill can cistern is 35 hours while outlet Pipe B can drain the filled cistern in 40 hours. The two pipes are opened together when the cistern is empty, but the outlet pipe is closed when the cistern is three-fifths full. How many hours did it take in all to fill the cistern?
Two inlet pipes P and Q can fill an empty tank in 5 hours and 4 hours respectively. There is an outlet pipe R in the tank which can empty the fully filled tank in 6 hours. Both the inlet pipes P and Q are opened to fill the empty tank, but after 3 hours it is observed that the outlet pipe is also open, immediately it is closed then find in how much time the tank will be completely filled after closing the outlet pipe R?