Multiple choice

A pipe can fill a tank in $x$ hours and another pipe can empty it in $y\left( y>x \right)$ hours. If both the pipes are open, in how many hours will the tank be filled?

  1. $\left( x-y \right)$
  2. $\left( y-x \right)$
  3. $\displaystyle\frac { xy }{ \left( x-y \right) }$
  4. $\displaystyle\frac { xy }{ \left( y-x \right) }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Rate of filling pipe = 1/x. Rate of emptying pipe = 1/y. Combined rate = 1/x - 1/y = (y - x) / xy. Time taken = 1 / (combined rate) = xy / (y - x).

AI explanation

The first pipe fills the tank at a rate of 1/x per hour, while the second pipe empties it at a rate of 1/y per hour. Because y is greater than x, the net filling rate when both are open is 1/x - 1/y = (y - x) / xy of the tank per hour. The total time to fill the tank is the reciprocal of the net rate, which is xy / (y - x) hours.

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