Multiple choice

A and B can together complete a piece of work in $10$ days and B and C in $20$ days. A works at it for $ 4$ days, B for $6$ days and C later completes it in $22$ days. The time taken by C alone to do the work is ?

  1. $20$ days
  2. $30$ days
  3. $40$ days
  4. $50$ days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given 1/A + 1/B = 1/10 and 1/B + 1/C = 1/20. Also 4/A + 6/B + 22/C = 1. Substituting 1/A = 1/10 - 1/B, we get 4(1/10 - 1/B) + 6/B + 22/C = 1, which simplifies to 2/B + 22/C = 0.6. Using 1/B = 1/20 - 1/C, we get 2(1/20 - 1/C) + 22/C = 0.6, so 20/C = 0.5, C = 40.

AI explanation

Let the daily work units of A, B, and C be a, b, and c respectively. We have a plus b equals 1/10 and b plus c equals 1/20. The equation for their combined individual work is 4 times a plus 6 times b plus 22 times c equals 1. Multiplying the second given equation by 6 gives 6b plus 6c equals 3/10, and subtracting this from the total work equation gives 4a minus 16c equals 7/10. Solving this with the first equation yields c equal to 1/40, meaning C alone takes 40 days.

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