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.
When all 3 pipes were opened simultaneously, volume of tank S filled in 1 hour is 3575 cubic meter. Pipe B alone can fill 25% of tank S in 3.5 hours. In how much time can pipe A fill 40% of tank S alone.
- A.
6 hours
- B.
4.8 hours
- C.
5.4 hours
- D.
2.8 hours
- E.
1.6 hours
Attempted by 3 students.
Show answer & explanation
Correct answer: D
Concept
Pipework problems run on additive flow rates. Express each pipe as a rate = (volume it moves) / (time it takes). An inlet adds volume (positive rate); an outlet removes volume (negative rate). When several pipes act together, the net rate is the algebraic sum of the individual rates, and time = (volume required) / (rate that acts).
Application
Work with Tank S, whose volume is 19250 cubic metres. Build each rate, then isolate pipe A:
Pipe B fills 25% of the tank in 3.5 hours, so it fills the whole tank in 3.5 / 0.25 = 14 hours; B's rate = 19250 / 14 = 1375 cubic metres per hour.
For Tank S the ratio of B's fill-time to C's empty-time is 2 : 5, so C's time = 14 x (5/2) = 35 hours; C's (outlet) rate = 19250 / 35 = 550 cubic metres per hour.
With all three open, the net filled in 1 hour is 3575 cubic metres, and net = A + B - C. So A = 3575 - 1375 + 550 = 2750 cubic metres per hour.
Therefore A alone fills the full tank in 19250 / 2750 = 7 hours.
Time for A to fill 40% = 0.40 x 19250 / 2750 = 7700 / 2750 = 2.8 hours.
Cross-check
Independent check: 40% of the 7-hour full-fill time is 0.40 x 7 = 2.8 hours, matching the rate computation. Also confirm the sign convention - because C is an outlet it is subtracted, which is why A must exceed the net to overcome both B's help and C's drain in the right balance.