Multiple choice

A and B can do a piece of work in 28 and 35 days respectively . They began to work together but A leaves after some time and B completed the remaining work in 17 days. After how much many days did A leave ?

  1. $\displaystyle 14\frac{2}{5}$ Days

  2. 9 Days

  3. 8 Days
  4. $\displaystyle 7\frac{5}{9}$
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C Correct answer
Explanation

B completes 17/35 of the work in 17 days, so the remaining work completed by A and B together is 18/35. Their combined daily rate is 1/28 + 1/35 = 9/140, and 18/35 divided by this rate equals 8 days.

AI explanation

Using the fraction method, B works for the entire duration and completes the remaining work in 17 days, meaning B's total work done is 17 divided by 35. The work done by A and B together is 1 minus 17/35, which equals 18/35. Since A and B's combined daily work rate is 1/28 plus 1/35, the least common multiple of 28 and 35 is 140, making their combined rate 5/140 plus 4/140, which equals 9/140 per day. The time they worked together is the completed fraction divided by their daily rate, so 18/35 divided by 9/140 equals 18/35 times 140/9, which simplifies to 8 days.

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