Multiple choice

Four pipes are required to fill a tank. The tank can be filled by first 3 pipes in 12 minutes, by last 3 pipes in 15 minutes and by the first and the fourth pipes in 20 minutes. How much time will be taken by all the four pipes to fill the tank?

  1. 8 minutes

  2. 10 minutes

  3. 12 minutes

  4. 15 minutes

  5. 20 minutes
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let rates be r1, r2, r3, r4. r1+r2+r3 = 1/12, r2+r3+r4 = 1/15, r1+r4 = 1/20. Summing these: 2(r1+r2+r3+r4) = 1/12 + 1/15 + 1/20 = (5+4+3)/60 = 12/60 = 1/5. So r1+r2+r3+r4 = 1/10. Time = 10 minutes.

AI explanation

Let the four pipes have individual filling rates of p, q, r, and s per minute. We are given the equations p+q+r = 1/12, q+r+s = 1/15, and p+s = 1/20. Adding the first two equations yields p+2q+2r+s = 3/20, and substituting 1/20 for (p+s) gives 2(q+r) + 1/20 = 3/20, meaning q+r = 1/20. Substituting q+r back into the first equation shows p = 1/12 - 1/20 = 1/30. The combined rate of all four pipes is (p+q+r) + s = 1/12 + (1/20 - p) = 1/12 + (1/20 - 1/30) = 1/12 + 1/60 = 6/60 = 1/10 per minute. Therefore, all four pipes working together will fill the tank in 10 minutes.

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