Multiple choice

There are two inlets A and B connected to a tank. A and B can fill the tank in 32 hours and 28 hours, respectively. If both the pipes are opened alternately for 1 hour, starting with A, then in how much time (in hours, to nearest integer) will the tank be filled?

  1. 22

  2. 30

  3. 36

  4. 24
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In 2 hours (one cycle of A then B), the tank fills 1/32 + 1/28 = 15/224 of the tank. After 28 cycles (56 hours), 28 * (15/224) = 15/8 = 1.875, which is impossible as the tank capacity is 1. We calculate the work done cycle by cycle until the tank is full, leading to 30 hours.

AI explanation

Using the LCM method, let the total capacity be 224 units, making the rates for pipe A and pipe B equal to 7 units per hour and 8 units per hour respectively. When opened alternately for 1 hour starting with A, they fill 15 units every 2 hours. After 28 hours of alternating work, they will have filled 14 cycles of 15 units, totaling 210 units and leaving 14 units empty. Pipe A will fill 7 units in the 29th hour, leaving 7 units for pipe B, which takes 7 divided by 8 of an hour to fill. The total time taken is 29.875 hours, which rounds to the nearest integer of 30.

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