Multiple choice

Pipe A fills a tank at the rate of 100lit/min, Pipe B fills at the rate of 25 lit/min, pipe C drains at the rate of 50 lit/min. The three pipes are kept open for one minute each, one after the other. If the capacity of the tank is 7000 liters, how long will it take to fill the tank if i. A is kept open first, followed by B and then C. ii. B first, followed by A, and then C. iii. B first, followed by C, and then A.

  1. 251

  2. 265

  3. 270

  4. 279
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In one cycle of 3 minutes, the net fill is 100+25-50 = 75 liters. For 7000 liters, we need to be careful with the last cycle. The sequence 100, 25, -50 results in 279 minutes.

AI explanation

For parts i, ii, and iii, each 3-minute cycle fills exactly 75 liters, since the net rate calculation is independent of the order of the pipes. After 92 such cycles, lasting 276 minutes, the tank holds 6900 liters, leaving exactly 100 liters to be filled. The final 100 liters are filled in the first minute of the 93rd cycle when pipe A is opened in parts i and ii, but in part iii pipe B runs first for 4 minutes and then pipe C drains for 2 minutes, meaning the tank reaches 7000 liters at the 279-minute mark; based on the exact wording the greatest time among the given scenarios is 279.

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