Multiple choice

Three pipes P1, P2 and P3 can fill a glass tub from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the glass tub is empty, all the three pipes are opened. P1,P2 and P3 discharge chemical solutions C, H and T respectively. What is the proportion of the solution T in the liquid in the pot after 3 minutes?

  1. 11/6

  2. 5/11

  3. 6/11

  4. 1/11

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In 3 minutes, P1 fills 3/30 = 1/10 of the tub, P2 fills 3/20, and P3 fills 3/10. Total volume = 1/10 + 3/20 + 3/10 = (2+3+6)/20 = 11/20. The proportion of T is (3/10) / (11/20) = (3/10) * (20/11) = 6/11.

AI explanation

Using the rate formula, pipes P1, P2, and P3 fill 1/30, 1/20, and 1/10 of the tank per minute, respectively. In 3 minutes, they fill 3/30, 3/20, and 3/10 of the tank, which equals 1/10, 3/20, and 3/10, respectively. The total liquid in the glass tub after 3 minutes is the sum of these parts, resulting in 1/10 + 3/20 + 3/10 = 11/20. Since pipe P3 represents the chemical solution T and contributes 3/10 of the tank, the proportion of T in the total liquid is (3/10) divided by (11/20), resulting in 6/11.

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