Multiple choice

A can do a piece of work in 40 days. A and B started doing the work, but midway through it, B got ill and was absent from work for 4 days. Due to this, the work was completed by both of them in 2 more days than the scheduled time. In how many days can A and B complete the piece of work?

  1. 18 days

  2. 20 days

  3. 22 days

  4. 24 days

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let A and B take x days. A's rate is 1/40. The work was completed in (x+2) days. A worked for (x+2) days, B worked for (x+2-4) = (x-2) days. Equation: (x+2)/40 + (x-2)/B = 1. Solving for B and then the combined rate shows 20 days is the correct answer.

AI explanation

Assume the scheduled completion time for A and B working together is D days, meaning their combined daily work rate is 1 over D. In the delayed scenario, B worked for D minus 4 days, while A worked for the entire D plus 2 days. The sum of their individual work done equals the total work, giving the equation (D minus 4 plus D plus 2) divided by D equals 1. Solving 2D minus 2 equals D results in D equaling 20 days.

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