Multiple choice

During Holi, two taps can fill a tub in 15 minutes and 20 minutes, respectively. Both the taps are opened at the same time, but after 4 minutes, first tap pipe is closed. In how much time will the tub be filled fully?

  1. 14 minutes and 40 seconds

  2. 12 minutes and 30 seconds

  3. 11 minutes and 45 seconds

  4. 10 minutes and 30 seconds

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

Tap 1 fills 1/15 per min, Tap 2 fills 1/20 per min. In 4 mins, they fill 4 * (1/15 + 1/20) = 4 * (7/60) = 7/15. Remaining = 8/15. Tap 2 fills this in (8/15) / (1/20) = 160/15 = 10.66 mins (10 min 40 sec). Total time = 4 + 10 min 40 sec = 14 min 40 sec.

AI explanation

Using the least common multiple method, let the total capacity of the tub be 60 units. The first tap fills 4 units per minute and the second tap fills 3 units per minute. In the first 4 minutes, both taps work together to fill (4 + 3) * 4 = 28 units, leaving 32 units. After the first tap is closed, only the second tap works to fill the remaining 32 units at a rate of 3 units per minute, which takes 32 / 3 minutes, or 10 minutes and 40 seconds. Adding the initial 4 minutes to this remaining time gives a total filling time of 14 minutes and 40 seconds.

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