Multiple choice

A can do a certain job in 25 days which B alone can do in 20 days. A started the work and was joined by B after 10 days. The work lasted for

  1. 25/2 days

  2. 128/9 days

  3. 15 days

  4. 50/3 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A's rate = 1/25, B's rate = 1/20. In 10 days, A completes 10/25 = 2/5 of the work. Remaining work = 3/5. Combined rate = 1/25 + 1/20 = 9/100. Time for remaining work = (3/5) / (9/100) = (3/5) * (100/9) = 20/3 days. Total time = 10 + 20/3 = 50/3 days.

AI explanation

Using the least common multiple method, let the total work be 100 units, meaning A completes 4 units per day and B completes 5 units per day. In the first 10 days, A alone completes 40 units, leaving 60 units of work. When A and B join forces, their combined daily output becomes 9 units. They will need 60 divided by 9 days to finish the job, making the total duration 50 divided by 3 days.

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