Multiple choice

$A$ and $B$ can separately do a piece of work in $20$ and $15$ days respectively. They worked together for $6$ days, after which $B$ was replaced by $C.$ If the work was finished in next $4$ days, then the number of days in which $C$ alone could do the work will be :

  1. $30$
  2. $35$
  3. $40$
  4. $60$
Reveal answer Fill a bubble to check yourself
C Correct answer
AI explanation

Using the Least Common Multiple method, let the total work be 60 units, making the daily work of A and B equal to 3 units and 4 units respectively. Working together for 6 days, they complete 42 units, leaving a remainder of 18 units. A and C finish this remaining 18 units in 4 days, meaning their combined daily rate is 4.5 units, so C's daily work is 1.5 units. Therefore, C alone would require 40 days to complete the total 60 units of work.

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