A and B together can do a work in 30 days and A alone can do it in 40 days. In how many days B alone can do this?
A and B together can do a work in 30 days and A alone can do it in 40 days. In how many days B alone can do this?
A120 days
B110 days
C80 days
D100 days
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Correct Answer: [120 days]
Explanation:
Let's determine how long B alone can complete the work.
Steps:
1. Let the total work be 1 unit.
2. A's work rate = \( \frac{1}{40} \) work/day (since A can complete the work in 40 days).
3. Combined work rate of A and B = \( \frac{1}{30} \) work/day (since together they can complete the work in 30 days).
4. B's work rate = Combined rate
- A's rate:
\(\frac{1}{30} - \frac{1}{40} = \frac{4}{120} - \frac{3}{120} = \frac{1}{120}\)
5. Therefore, B alone can complete the work in \( 120 \) days.Final Answer: \(\boxed{120}\)
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