Multiple choice

$A$ does $\displaystyle \frac{4}{5}$th of 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. $\displaystyle 37\frac{1}{2}$ days
  4. $40$ days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Since A completes 4/5 of the work in 20 days, A can complete the entire work alone in 25 days, meaning A's daily work rate is 1/25. The remaining 1/5 of the work is completed by A and B together in 3 days, which means their combined daily rate is 1/15. Subtracting A's rate from the combined rate gives B's daily rate as 1/15 - 1/25 = 2/75, so B alone takes 75/2 = 37 1/2 days.

AI explanation

If A completes 4 fifths of the work in 20 days, the efficiency method shows A's daily work rate is 1 twenty-fifth, meaning A alone would take 25 days. The remaining work is 1 fifth, which A and B finish in 3 days, meaning their combined daily rate is 1 fifteenth. Subtracting A's rate of 1 twenty-fifth from their combined rate of 1 fifteenth gives B's daily rate as 2 over 75, so B alone takes 75 divided by 2 days, which is 37 and a half days.

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