Direction : Read the given below table carefully and answer the following…
2021
Direction : Read the given below table carefully and answer the following questions.
The data shows volume and height of 4 right circular tanks P, Q, R and S. The given data also depicts time taken to fill or empty the tank by inlet pipe A, B and outlet pipe C.
1. Ratio between time taken by pipe B and that by pipe C is different because pipes were used by the operator in different ways for different tanks.
2. Radius of tank S is 10.5 m.
In tank R, pipe A was opened for 9 hours and then closed. Pipe B and C were the opened together for 3 hours and then both pipes were closed. After a total of 12 hours, approximately what volume of tank remained empty (in cubic meters), if both pipes A and C were opened together, tank will always be empty).
- A.
775 𝑚3
- B.
840 𝑚3
- C.
900 𝑚3
- D.
1020 𝑚3
- E.
960 𝑚3
Show answer & explanation
Correct answer: C
Concept
For a tank, fill/empty rate = (tank volume) / (time to fill or empty completely). When an inlet and an outlet run together, the net change per hour = (inlet rate) - (outlet rate). If an inlet and an outlet exactly cancel, the net rate is zero, so a tank that starts empty stays empty.
Given (Tank R)
Volume = 5390 m3, filled fully by pipe A in 18 hours.
Statement: with pipes A and C open together the tank always stays empty, so pipe C empties at exactly the same rate as pipe A fills (their effects cancel). Hence pipe C empties the full tank in 18 hours too.
Ratio of time taken by pipe B (to fill) to pipe C (to empty) = 1 : 3, so pipe B fills the full tank in 18/3 = 6 hours.
Working
Rate of A = 5390 / 18 m3/h. In the first 9 hours only A runs, so water added = 9 x (5390/18) = 2695 m3.
Rate of B = 5390 / 6 m3/h and rate of C = 5390 / 18 m3/h. With B and C open together (A closed), net inflow per hour = 5390/6 - 5390/18 = 5390 x (3 - 1)/18 = 5390 x 2/18 m3/h.
Over the next 3 hours, water added = 3 x 5390 x 2/18 = 5390/3 = 1796.67 m3.
Total water in the tank after 12 hours = 2695 + 1796.67 = 4491.67 m3.
Volume left empty = 5390 - 4491.67 = 898.33 m3, which is approximately 900 m3.
Cross-check
A fills 2695 m3 in 9 h (half the tank, since A alone needs 18 h). In the next 3 h the net fill rate equals two-thirds of A's rate, adding 5390/3 m3. The filled total 4491.67 m3 leaves 898.33 m3 empty, rounding to 900 m3.