Multiple choice

Two pipes A and B can fill a tank in 12 minutes and 16 minutes, respectively. Both are kept open for 'n' minutes and then B is closed. A fills the rest of the tank in 5 minutes. The value of n is

  1. 4

  2. 5

  3. 2

  4. 3

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

Pipe A fills 1/12 per minute and B fills 1/16 per minute. Together they fill (1/12 + 1/16) = 7/48 per minute. For n minutes, they fill 7n/48. A then fills the remaining part in 5 minutes, which is 5/12. Equation: 7n/48 + 5/12 = 1. Solving for n gives 7n/48 = 7/48, so n = 4.

AI explanation

Using the least common multiple method, let the total capacity of the tank be 48 units. Pipe A fills at 4 units per minute and pipe B fills at 3 units per minute. In the first n minutes, both pipes are open, filling 7 units per minute for a total of 7n units. After pipe B is closed, pipe A fills the rest in 5 minutes, adding 4 times 5 or 20 units. The equation for the full tank is 7n plus 20 equals 48. Solving for n gives 7n equals 28, so n is 4. The answer is 4.

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