Multiple choice

Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes?

  1. 8/11

  2. 7/11

  3. 6/11

  4. 5/11
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Rates: A=1/30, B=1/20, C=1/10. In 3 minutes: A fills 3/30=1/10, B fills 3/20, C fills 3/10. Total filled = 1/10 + 3/20 + 3/10 = 2/20 + 3/20 + 6/20 = 11/20. The proportion of R (from C) is (3/10) / (11/20) = (6/20) / (11/20) = 6/11.

AI explanation

Using the work and time method, the parts of the tank filled by pipes A, B and C in one minute are 1/30, 1/20 and 1/10 respectively. When all three pipes are open for 3 minutes, the proportion of solution P is 3/30, solution Q is 3/20 and solution R is 3/10. The total liquid in the tank after 3 minutes is the sum of these parts, which is 1/10 + 3/20 + 3/10 = 2/20 + 3/20 + 6/20 = 11/20. The proportion of solution R is (3/10) divided by (11/20), which equals 6/11.

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