Multiple choice

A tank connected with 15 pipes, some of them are inlet pipes, and the rest work as outlet pipes. Each of the Inlet pipes can fill the tank in 8 hour individually while each of those that drain the tank can drain it in 6 hours individually. If all the pipes are kept open when the tank is full. It will take exactly 6 hour for the tank to empty. How many of these are Inlet pipes?

  1. 4

  2. 8

  3. 3

  4. 6

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

Let x be the number of inlet pipes. Then 15-x are outlet pipes. The rate of filling is x/8 and the rate of emptying is (15-x)/6. The net rate is -1/6 (since it empties in 6 hours). So, x/8 - (15-x)/6 = -1/6. Multiplying by 24 gives 3x - 4(15-x) = -4, so 3x - 60 + 4x = -4, 7x = 56, x = 8.

AI explanation

Let the number of inlet pipes be x, meaning the number of outlet pipes is 15 minus x. The combined rate of all pipes working together to empty the full tank in 6 hours is negative one-sixth of the tank per hour. Setting up the equation based on individual rates, x divided by 8 minus the quantity 15 minus x divided by 6 equals negative one-sixth. Solving this equation, 3x minus 60 plus 4x equals negative 4, which leads to 7x equals 56; therefore, the number of inlet pipes is 8.

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