Multiple choice

Pipe X can fill the reservoir in 20 hours, and pipe Y can fill it in 30 hours. A drain pipe Z can empty the full reservoir in y hours. All three pipes were opened simultaneously at 6:00 a.m, and the drain pipe Z was closed at 12:00 p.m. The reservoir was completely filled by 8:00 p.m. Find the value of y.

  1. 20

  2. 24

  3. 36

  4. 40
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let reservoir capacity = 60 units. Rate X = 3, Rate Y = 2, Rate Z = -60/y. Pipes X, Y, Z open for 6 hours (6am to 12pm): 6 * (3 + 2 - 60/y) = 30 - 360/y. Remaining work = 60 - (30 - 360/y) = 30 + 360/y. Pipes X, Y open for 8 hours (12pm to 8pm): 8 * (3 + 2) = 40. So 30 + 360/y = 40 => 360/y = 10 => y = 36.

AI explanation

Operating from 6:00 a.m. to 12:00 p.m., all three pipes work for 6 hours, followed by 8 hours of only pipes X and Y working from 12:00 p.m. to 8:00 p.m. The net fraction filled in the first 6 hours is 6 times the sum of (1/20) + (1/30) minus (1/y), which simplifies to (1/2) minus (6/y). The fraction filled in the next 8 hours by pipes X and Y is 8 times the sum of (1/20) + (1/30), which equals 2/3. Equating the total filled fraction to 1 gives the equation (1/2) minus (6/y) plus 2/3 = 1, which simplifies to 6/y = 1/6, yielding y = 36.

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