Bissoy.com
Doctors Medicines MCQs Q&A

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?

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? Correct Answer 12 hours

Suppose the time taken to fill the first half of the tank in the first situation = ‘a’ hours

Time taken to fill the second half of the tank in the first situation = ‘b’ hours

a + b = 18 hours      ----(1)

If the time taken by only the inlet pipe to fill half part of the tank is ‘a’ hours, then the time taken by the inlet pipe to fill the (2/3)rd part of the tank = (4/3)a hours

If the time taken by the inlet and outlet pipes together to fill half part of the tank is ‘b’ hours, then the time taken by both of them to fill the remaining (1/3)rd part of the tank in the second scenario = (2/3)b hours

(4/3)a + (2/3)b = 16      ----(2)

Solving equation 1 and 2, we get a = 6, b = 12

Time taken by the inlet pipe to fill half the tank = 6 hours

∴ Time taken by the inlet pipe to fill full tank = 12 hours

Related Questions

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 inlet pipe and an outlet pipe. If the outlet pipe is closed then the inlet pipe fills the empty tank in 8 hours. If the outlet pipe is open then the inlet pipe fills the empty tank in 10 hours. If only the outlet pipe is open then in how many hours the full tank becomes half-full?
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: There are two inlet pipes A, B and two outlet pipes C, D inlet pipe B takes 7 hours more to fill the tank when compared to A. Two outlet pipes when working together can empty the tank in 3.5 hours and efficiency of both the pipe is same if all of them working together can fill the tank in 2 hours. Calculate the time taken by A to fill the tank. Quantity B: The ratio of efficiencies of two pipes A and B is in the ratio 3 ∶ 2 and that of pipe B and C is 1 ∶ 3. Pipe A and B are inlet pipes, pipe C is outlet pipe working together they can fill the tank in 7.5 hours. Calculate the time taken by A to fill the tank when working alone.
A tank has an inlet and outlet pipe. The inlet pipe fills the tank completely in 2 hours when the outlet pipe is plugged. The outlet pipe empties the tank completely in 6 hours when the inlet pipe is pluggeed. If there is a lekage also which is capable of draining out the liquid from the tank at half of the rate of outet pipe,them what is the time taken to fill the emty tank when both the pipes are opened?
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?
The following questions have three statements. Study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. In how many hours tap B can fill the completely empty tank? Statement I: The inlet tap A and the outlet tap C working simultaneously takes 40 hours to fill the tank. Statement II: Efficiency of inlet tap B is equal to efficiency of outlet tap C or 62.5% of the efficiency of inlet tap A. Statement III: The outlet tap C can empty a half filled tank in 12 hours.
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?
There are two pipes T and V which can empty the tank and one pipe S can fill the tank. Pipe S can fill the tank in 5 hours. Pipe T can empty half of the tank in 5 hours. Pipe S is opened for 1 hour and 15 min then Pipe T and Pipe V are also opened. Then the (remaining) tank gets filled in 10 hours. In what time pipe V can empty the 1/4th filled tank?
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?