Multiple choice

Pipes A and B can fill a tank in 60 minutes and 40 minutes, respectively. How much time will it take to fill the tank, if pipe B is used for half the time and then, pipes A and B together fill the tank for the rest of the time?

  1. 26 minutes

  2. 30 minutes

  3. 32 minutes

  4. 33 minutes

  5. 35 minutes
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let T be total time. B works for T/2. A and B work together for T/2. Rate A = 1/60, Rate B = 1/40. (T/2 * 1/40) + (T/2 * (1/60 + 1/40)) = 1. T/80 + T/2 * (5/120) = 1. T/80 + T/48 = 1. (3T + 5T)/240 = 1. 8T = 240, T = 30.

AI explanation

Using the LCM method, let the total capacity be 120 units, making the filling rates of pipes A and B equal to 2 and 3 units per minute respectively. Let the total time taken be x minutes, meaning pipe B works for the entire duration while pipes A and B work together for the second half. The equation is 3x divided by 2 plus 5x divided by 2 equals 120, which simplifies to 4x equals 120, giving a total time of 30 minutes.

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