Multiple choice

A' alone can do a piece of work in 24 days. If his friend 'B' joins him for the first 4 days, the work is finished in 6 days less. How many days will B alone take to do the work?

  1. 12 days

  2. 15 days

  3. 16 days

  4. 18 days

  5. 20 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A does the work in 24 days, so A's rate is 1/24 per day. The work is finished in 24 - 6 = 18 days. In 18 days, A does 18/24 = 3/4 of the work. B must have done the remaining 1/4 of the work in the first 4 days. B's rate is (1/4) / 4 = 1/16, so B takes 16 days.

AI explanation

Using the total work method, let the total work be 24 units, meaning A completes 1 unit per day. If B joins A for the first 4 days and the total time is reduced by 6 days from 24 to 18 days, A works alone for 14 days to complete 14 units. The remaining 10 units of work must have been completed by A and B working together during those first 4 days, meaning their combined daily work is 2.5 units. Subtracting A's 1 unit from the combined 2.5 units leaves 1.5 units completed by B each day, so dividing the total 24 units by 1.5 units per day yields the result of 16 days.

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