Multiple choice

A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?

  1. 15 days

  2. 12 days

  3. 10 days

  4. 9 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A's rate is 1/12, B's rate is 1/16. In 3 days, they complete 3 * (1/12 + 1/16) = 3 * (7/48) = 21/48 = 7/16 of the work. Remaining work is 9/16. B completes this in (9/16) / (1/16) = 9 days.

AI explanation

Using the fraction of work method, let the total work be the least common multiple of 12 and 16, which is 48 units. A's rate is 4 units per day and B's rate is 3 units per day, so their combined rate is 7 units per day. Working together for 3 days, they complete 21 units, leaving 27 units of remaining work. B alone completes the 27 units at a rate of 3 units per day, requiring 27 divided by 3 days. The result is 9 days.

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