Direction: Read the table given below carefully and answer the following…
2021
Direction: Read the table given below carefully and answer the following question.
The data shows the volume and height of 4 right circular (cylindrical) tanks P, Q, R and S. The data also depicts the time taken to fill or empty each tank by inlet pipes A and B and outlet pipe C.
1. The ratio between the time taken by pipe B and that taken by pipe C is different for different tanks because the operator used the pipes in different ways.
2. The radius of tank S is 10.5 m.
In tank R (starting from empty), pipe A was opened for 9 hours and then closed. Pipes B and C were then opened together for 3 hours and then both were closed. After a total of 12 hours, approximately what volume of the tank remained empty (in cubic metres)? (Note: pipes A and C together keep the tank at the same level, i.e. outlet C empties at exactly the rate at which inlet A fills.)
- A.
775 m3
- B.
840 m3
- C.
900 m3
- D.
1020 m3
- E.
960 m3
Attempted by 1 students.
Show answer & explanation
Correct answer: C
Concept
For a pipe that fills (or empties) a tank of volume V in T hours, its rate of working is V/T per hour. When a filling pipe and an emptying pipe run together, the net change per hour is (fill rate − empty rate). If a fill pipe and an empty pipe have equal rates, the net rate is exactly zero and the water level does not change.
Setting up the rates for tank R
Volume of tank R, V = 5390 m3. Pipe A fills it in 18 h, so A's fill rate = 5390 ÷ 18 ≈ 299.44 m3/h.
Pipes A and C together keep the level unchanged, so outlet C empties at exactly A's fill rate of 299.44 m3/h; hence C empties the full tank in 18 h, i.e. time for C = 18 h.
The given ratio (time of B) : (time of C) = 1 : 3, so time for B = 18 ÷ 3 = 6 h, giving B's fill rate = 5390 ÷ 6 ≈ 898.33 m3/h.
Applying the 12-hour schedule (tank starts empty)
Phase 1 — A alone for 9 h: water added = 299.44 × 9 = 2695 m3.
Phase 2 — B and C together for 3 h: net fill rate = 898.33 − 299.44 = 598.89 m3/h, so water added = 598.89 × 3 ≈ 1796.67 m3.
Total water after 12 h = 2695 + 1796.67 = 4491.67 m3.
Empty volume remaining = V − filled = 5390 − 4491.67 = 898.33 ≈ 900 m3.
Cross-check
The two phases add ≈4491.67 m3 to an empty 5390 m3 tank — about 83% full — so the remaining ≈17% is 898.33 m3, which rounds to 900 m3.