Multiple choice

$A$ can do a piece of work in $80$ days. He works at it for $10$ days and then $B$ alone finishes the work in $42$ days. The two together could have completed the work in _________.

  1. $24\ days$
  2. $25\ days$
  3. $30\ days$
  4. $35\ days$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A does 1/80 per day. In 10 days, A does 10/80 = 1/8. Remaining work = 7/8. B does 7/8 in 42 days, so B does 1/48 per day. Together, they do 1/80 + 1/48 = (3+5)/240 = 8/240 = 1/30. They finish in 30 days.

AI explanation

Using the LCM method, let the total work be 80 units, so A completes 1 unit per day. In 10 days, A completes 10 units, leaving 70 units for B to finish in 42 days, meaning B completes 70 divided by 42, or 5/3 units per day. Their combined rate is 1 plus 5/3, which equals 8/3 units per day. Dividing the total 80 units by 8/3 gives 30 days. Working together, they complete the work in 30 days.

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