Multiple choice

$A$ does $80$% of a work in $20$ days. He then calls in $B$ and they together finish the remaining work in $3$ days. How long $B$ alone would take to do the whole work?

  1. $23$ days
  2. $37$ days
  3. $37\cfrac{1}{2}$
  4. $40$ days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A does 80% in 20 days, so A's rate is 4% per day. Remaining 20% is done by A and B in 3 days, so (A+B)'s rate is 20/3 = 6.66% per day. B's rate = 6.66 - 4 = 2.66% per day. Time for B = 100 / 2.66 = 37.5 days.

AI explanation

A completes 80% of the work in 20 days, meaning A would complete 100% of the work in 25 days, giving A a daily work rate of 1/25. The remaining work is 20%, or 1/5 of the total job, which A and B finish in 3 days; their combined daily rate is (1/5) divided by 3, which equals 1/15. Subtract A's rate from their combined rate to find B's rate: 1/15 - 1/25 = (5-3)/75 = 2/75. Therefore, B alone would take the reciprocal of 2/75 to complete the work, which is 37 and 1/2 days.

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