Multiple choice

Three pipes A, B and C can fill a tank in 6 min, 8 min, and 12 min. respectively. The pipe C is closed for 4 min before the tank is filled. In what time would the tank be fill ?

  1. $\displaystyle 3\frac{5}{9}$ min.
  2. $\displaystyle 5\frac{5}{9}$ min.
  3. $\displaystyle 5\frac{3}{9}$ min.
  4. $\displaystyle 4\frac{5}{9}$ min.
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A Correct answer
AI explanation

Let the total time to fill the tank be t minutes; pipe C works for (t - 4) minutes while A and B work for t minutes. The work equation is t/6 + t/8 + (t - 4)/12 = 1. Multiplying by 24 gives 4t + 3t + 2t - 8 = 24, which simplifies to 9t = 32 or t = 32/9. Converting this improper fraction gives 3 and 5/9 minutes. The result is 3 and 5/9 min.

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