Multiple choice

$A$ completes a work in $12$ days. $B$ completes the same work in $15$ days. $A$ started working alone and after $3$ days $B$ joined him. How many days will they now take together to complete the remaining work?

  1. $6$
  2. $8$
  3. $5$
  4. $4$

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

A's rate is 1/12, B's is 1/15. A works alone for 3 days, completing 3/12 = 1/4 of the work. Remaining work is 3/4. Combined rate is 1/12 + 1/15 = 9/60 = 3/20. Time taken = (3/4) / (3/20) = 5 days.

AI explanation

Using the LCM method, the total work is the least common multiple of 12 and 15 days, which is 60 units. A's efficiency is 5 units per day and B's efficiency is 4 units per day. In the first 3 days, A works alone and completes 15 units, leaving 45 units of work remaining. When A and B work together, their combined efficiency is 9 units per day. They will take 45 divided by 9, which equals 5 days to complete the remaining work.

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