Multiple choice

A. B and C together can do a piece of work in $40$ days. After working with B and C for $16$ days, A leaves and then B and C complete the remaining work in $40$ days more. A alone could do the work in

  1. $80$ days
  2. $90$ days
  3. $100$ days
  4. $120$ days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A, B, and C together complete 1/40 of the work per day. In 16 days they complete 2/5, leaving 3/5 for B and C, which they finish in 40 days, so their rate is 3/200 per day. A's rate is therefore 1/40 - 3/200 = 1/100, so A alone needs 100 days.

AI explanation

Let the total work be 1 unit, where the combined rate of A, B, and C is 1/40 per day. In the first 16 days, A, B, and C complete 16/40 or 2/5 of the work, leaving 3/5 of the work. B and C complete this remaining 3/5 of the work in 40 days, so their combined daily rate is (3/5) divided by 40, which equals 3/200. Subtracting the rate of B and C from the rate of A, B, and C gives A's daily rate as 1/40 minus 3/200, which equals 1/100, meaning A alone can do the work in 100 days.

Keep practicing — related questions