Multiple choice

A and B can together finish a work in $30$ days. They worked together for $20$ days and then B left. After another $20$ days A finished the remaining work. The number of days in which B alone can finish the work is

  1. $50$
  2. $48$
  3. $54$
  4. $60$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let A and B's work rates be a and b. Given 30(a+b) = 1 (total work). They worked together for 20 days: 20(a+b) = 2/3 of work. Remaining work 1/3 was done by A in 20 days, so A's rate is (1/3)/20 = 1/60. Since a+b = 1/30, then b = 1/30 - 1/60 = 1/60. Thus, B takes 60 days.

AI explanation

Taking the total work as the least common multiple of the days gives 60 units, making the combined rate of A and B equal to 2 units per day. When they work together for 20 days, they complete 40 units of work, leaving 20 units for A to finish alone in 20 days. This establishes A's daily work rate as 1 unit per day. Subtracting A's rate from their combined rate gives B's daily rate as 1 unit per day, so B alone can finish the 60 units of work in 60 days.

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