Multiple choice

A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 4 days B had to leave. Then A working with a new worker C completed the remaining work in 3 days. If C works alone, in how many days he can do 40% of the same work?

  1. 9

  2. 10

  3. 8

  4. 8.5
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A Correct answer
Explanation

A's 1 day work = 1/15, B's = 1/10. In 4 days together: 4(1/15+1/10) = 4(5/30) = 2/3. Remaining = 1/3. A + C do 1/3 in 3 days, so (1/15 + 1/C) × 3 = 1/3, giving 1/C = 2/45. C alone does full work in 22.5 days. 40% of work = 0.4 × 22.5 = 9 days. The key is finding C's rate from the combined work rate.

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