Multiple choice

A and B, each working alone, can do a work in 15 days and 25 days, respectively. They start the work together, but B leaves after some time and A finishes the remaining work in 7 days. How many days after the start of work does B leave?

  1. 7

  2. 9

  3. 3

  4. 5
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A's rate is 1/15 and B's rate is 1/25. Let B work for x days. Then (1/15 + 1/25)x + (1/15)7 = 1. (8/75)x + 7/15 = 1. (8/75)x = 8/15. x = (8/15)(75/8) = 5 days.

AI explanation

Taking the total work as the least common multiple of 15 and 25, which is 75 units, the daily work of A is 5 units and the daily work of B is 3 units. Since A works alone for the last 7 days, he completes 35 units, leaving 40 units of work to be done by A and B together. Their combined daily work is 8 units, so they worked together for 5 days (40 divided by 8); therefore, B leaves after 5 days.

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