Multiple choice

A , B and C together can complete a piece of work in $10$ days. All the three started working at it together and after $4$ days A left. Then B and C together completed the work in $10$ more days. A alone could complete the work in :

  1. $15$  days
  2. $16$  days
  3. $25$ days
  4. $50$  days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A+B+C = 1/10 per day. In 4 days, they do 4/10 = 2/5 of the work. Remaining work = 3/5. B+C do 3/5 in 10 days, so B+C = (3/5)/10 = 3/50 per day. A = (A+B+C) - (B+C) = 1/10 - 3/50 = 5/50 - 3/50 = 2/50 = 1/25. A takes 25 days.

AI explanation

Let the total work be the LCM of 10 and 10, which is 10 units, so A, B, and C together work at 1 unit per day. In the first 4 days, they complete 4 units, leaving 6 units of work. B and C complete these remaining 6 units in 10 days, meaning their combined daily rate is 6/10 or 3/5 units per day. A's daily rate is the total rate (1) minus B and C's rate (3/5), which is 2/5 units per day. Therefore, A alone would take 10 divided by 2/5, which equals 25 days to complete the work.

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