A and B together can complete a work in 3 days. They start together but after 2 days, B left the work. If the work is completed after two more days, B alone could do the work in ____?
Maths / Direction Sense MCQs — Multiple-choice practice
- A. 9 days
- B. None of these
- C. 6 days
- D. 5 days
Correct answer
6 days
Explanation
Explanation A and B together can complete the work in 3 days, so their combined rate of work is 1/3 per day. They work together for 2 days, so they complete 2/3 of the work. B leaves, and A completes the remaining 1/3 of the work in 2 days. This means A's rate of work is 1/6 per day (since A completes 1/3 of the work in 2 days). Now, we know B's rate of work is the difference between their combined rate and A's rate: (1/3 - 1/6) = 1/6 per day. Since B can complete the entire work in x days, B's rate of work is also 1/x per day. Equating the two expressions for B's rate of work, we get: 1/6 = 1/x --> x = 6 So, B alone can complete the work in 6 days.
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