Multiple choice

Pipe M and N running together can fill a cistern in 6 minutes. If M takes 5 minutes less than N to fill the cistern, then the time in which N alone can fill the cistern will be

  1. $15$ min
  2. $20$ min
  3. $25$ min
  4. $10$ min
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

1/M + 1/N = 1/6. M = N - 5. 1/(N-5) + 1/N = 1/6. (N + N - 5) / (N(N-5)) = 1/6. 6(2N - 5) = N^2 - 5N. 12N - 30 = N^2 - 5N. N^2 - 17N + 30 = 0. (N-15)(N-2) = 0. N = 15.

AI explanation

Let the time taken by pipe N be x minutes, so the time taken by pipe M is (x - 5) minutes. The sum of their individual rates equals their combined rate, so 1/x plus 1/(x - 5) equals 1/6. Multiplying by the common denominator yields the quadratic equation 6x plus 6 times (x - 5) equals x squared minus 5x, which simplifies to x squared minus 17x plus 30 equals 0. Factoring this gives (x - 15) times (x - 2) equals 0, and since x must be greater than 5, the valid solution is 15 minutes.

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