Multiple choice

A does $\dfrac { 4 } { 5 }$ of a work in $20$ days. He then calls in $\mathrm { B }$ and they together finish the remaining work in $3$ days. How long $\mathrm { B }$ alone would take to do the whole work?

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

A does 4/5 in 20 days, so A's rate is (4/5)/20 = 1/25 per day. Remaining work = 1/5. A and B finish 1/5 in 3 days, so their combined rate is (1/5)/3 = 1/15. B's rate = Combined - A = 1/15 - 1/25 = (5-3)/75 = 2/75. B takes 75/2 = 37.5 days.

AI explanation

If A completes 4/5 of the work in 20 days, the unitary method shows A completes the whole work in 20 divided by 4/5, which equals 25 days. The remaining work is 1/5, which A and B finish in 3 days; their combined daily rate is (1/5) divided by 3, equaling 1/15. Subtracting A's daily rate of 1/25 from 1/15 gives B's daily rate of 1/15 minus 1/25, which equals 2/75. Therefore, B alone takes 75 divided by 2, or 37 and 1/2 days.

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