Multiple choice

$A$ and $B$ can do a work in $10$ days. $B$ and $C$ can do the same work in $15$ days. $C$ and $A$ can complete the same work in $20$ days. In how many days can $C$ alone complete the work ?

  1. $120$ days
  2. $118$ days
  3. $115$ days
  4. $110$ days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A, B, C be the work done per day. A+B=1/10, B+C=1/15, C+A=1/20. Adding these: 2(A+B+C) = 1/10 + 1/15 + 1/20 = (6+4+3)/60 = 13/60. So A+B+C = 13/120. C = (A+B+C) - (A+B) = 13/120 - 1/10 = 1/120. C takes 120 days.

AI explanation

Adding the combined one-day work rates gives (1/10) + (1/15) + (1/20) = 2(A + B + C). The right side equals 6/60 + 4/60 + 3/60 = 13/60, so the combined rate of A, B and C is 13/120 per day. Subtracting the combined rate of A and B (1/10 or 12/120) from this total gives C's rate: 13/120 - 12/120 = 1/120 per day. Therefore, C alone takes 120 days to complete the work. The correct result is 120 days.

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