Multiple choice

I can do a piece of work in 8 days, which can be done by you in 10 days. How long would it take to do it if we work together?

  1. $4\displaystyle\frac{4}{9}$ days
  2. $5\displaystyle\frac{3}{9}$ days
  3. $5\displaystyle\frac{1}{2}$ days
  4. $4\displaystyle\frac{7}{9}$ days
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A Correct answer
Explanation

Work done by me in 1 day = 1/8. Work done by you in 1 day = 1/10. Together = 1/8 + 1/10 = (5+4)/40 = 9/40. Time = 40/9 = 4 4/9 days.

AI explanation

Using the LCM method for Time and Work, let the total work be the least common multiple of 8 and 10, which is 40 units. The first person completes 5 units per day and the second person completes 4 units per day. Working together, their combined rate is 9 units per day, so dividing 40 by 9 gives 4 and 4/9 days. The work takes 4 and 4/9 days.

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