Multiple choice

A can do a work in x days and B can do the same work in y days then the number of days taken by A and B together to complete the work are

  1. $\displaystyle \frac{y}{x+y}$ days
  2. $\displaystyle \frac{x}{x+y}$ days
  3. $\displaystyle \frac{xy}{x+y}$ days
  4. $\displaystyle \frac{xy}{x-y}$ days
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C Correct answer
Explanation

A's rate is 1/x and B's rate is 1/y. Combined rate is (1/x + 1/y) = (x+y)/xy. The time taken is the reciprocal of the combined rate, which is xy/(x+y).

AI explanation

Using the LCM method for Time and Work, if A takes x days and B takes y days, their individual rates are 1/x and 1/y of the work per day. Adding their rates gives a combined rate of (y plus x) divided by xy. The reciprocal of this combined rate provides the total time, which is xy divided by (x plus y) days. The correct time taken is xy divided by (x plus y) days.

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