A does half as much work as B in one-sixth of the time. If together they take 10 days to complete a work, how much time shall B alone take to do it?a)70 daysb)30 daysc)40 daysd)50 daysCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Given information:
A does half as much work as B in one-sixth of the time.
Together they take 10 days to complete the work.

Let's Assume:
Let's assume that B takes x days to complete the work alone.

Calculating Work Rates:
- A's work rate = 1/(6x) (since A does half as much work as B in one-sixth of the time)
- B's work rate = 1/x (work completed by B in one day)

Work Rate Equation:
Given that together they take 10 days to complete the work:
1/(6x) + 1/x = 1/10
Solving the above equation, we get:
x = 40 days

Conclusion:
Therefore, B alone would take 40 days to complete the work. Hence, the correct answer is option 'C'.

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