CTET Maths MCQ - Time and Work

6 Pipe A can fill a cistern in 36 minutes and B in 48 minutes. If both the pipes are opened together, when should pipe B be closed so that the cistern may be just full in 24 minutes?

Let pipe B be turned off after x minutes.

⇒ x = 16 minutes

7 Pipes P, Q and R are attached to a tank and each can act as either an inlet or outlet pipe. Pipes P, Q and R respectively take 8, 10 and 12 hours to fill the empty tank or empty the full tank. In the first hour, pipes P and R work as inlet and Q work as outlet. In the second hour, pipes P and Q work as inlet and pipe R as outlet. In the third hour pipes Q and R work as inlet and pipe P as outlet and the process goes on like this. When will the cistern be filled?

In a cycle of 3 hours: pipes P, Q and R are working as inlet pipes for 2 hours each and they are working as outlet pipes for an hour each. So part of tank filled in 3 hours.

Thus, tank will be filled in 10th hour.

8 There are 2 inlet pipes and an outlet pipe. The efficiency of one of the inlet pipes is double than that of the other. Also, the efficiency of the outlet pipe is half that of the lesser efficient inlet pipe. The empty tank gets filled in 16 hours when all the pipes are opened. How many hours will be taken to fill the empty tank when the 'lesser' efficiency inlet pipe is plugged and the rest kept opened?

Let number of hours taken by the outlet and the 2 inlet pipes be 4x, 2x and x respectively.
So in 1 hour the part of empty tank filled is

Hence, inlet pipe with higher efficiency fills the tank in 20 hours.
So in one hour, the desired pipes fill

Refer to the data below and answer the questions that follow.
The boiler tank in a chemical factory holds 10⁵ litres. 5 tanks each having one-fifth the capacity of the boiler tank fill in ‘hard water’ at same rates in the boiler tank in 2 hours. The outlet of the two of smaller tanks work as inlet pipes and other two work as outlet and the fifth tank fill in the main ‘boiler’ at half its efficiency.

9 What is the number of hours taken to fill in the main boiler when all the pipes are opened at once?

Since 5 tanks of same efficiency fill the boiler in 2 hours each tank individually takes
2 x 5 = 10 hours to fill it.
Tank with half the efficiency will take 10 x 2 = 20 hours.
In one hour, fraction of boiler getting filled when 4 fully efficient pipes with two as inlet and two as outlet and 5th acts at 50% efficiency as an inlet is

Hence it will take 20 hours to fill the boiler tank.

Refer to the data below and answer the questions that follow.
The boiler tank in a chemical factory holds 10⁵; litres. 5 tanks each having one-fifth the capacity of the boiler tank fill in ‘hard water’ at same rates in the boiler tank in 2 hours. The outlet of the two of smaller tanks work as inlet pipes and other two work as outlet and the fifth tank fill in the main ‘boiler’ at half its efficiency.

10 Only three pipes are working, two at their full efficiency and the third one with half of its efficiency and all three are acting as an inlet. If all the three are opened alternately with the latter pipe being first to be opened to fill the boiler such that each smaller tank fills 'hard water' in the main boiler for equal time, then number of hours taken to fill the boiler to half its capacity is

Here fraction of tank filled in 1 hour

th of the tank
If they are opened alternately, then tank gets filled in 4 x 3 = 12 hours
Hence half of the tank gets filled in 12/2 = 6 hours.

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