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Select the correct answerA does half as much work as B in three-fourth of the time. If together they take 18 days to complete a work. How much time shall B take to do it alone?Options35 days30 days40 days45 days

Question

Select the correct answerA does half as much work as B in three-fourth of the time. If together they take 18 days to complete a work. How much time shall B take to do it alone?Options35 days30 days40 days45 days

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Solution

To solve this problem, we need to understand the concept of work and time.

Step 1: Let's assume the amount of work to be 1 (for simplicity).

Step 2: Let's say B takes 'x' days to complete the work. So, B's work rate is 1/x (work/day).

Step 3: According to the problem, A does half as much work as B in three-fourth of the time. So, A's work rate is (1/2) * (1/x) / (3/4) = 2/(3x) (work/day).

Step 4: Together, A and B can complete the work in 18 days. So, their combined work rate is 1/18 (work/day).

Step 5: We can set up the equation 1/x + 2/(3x) = 1/18.

Step 6: Solving this equation, we get x = 30.

So, B alone would take 30 days to complete the work. Therefore, the correct answer is 30 days.

This problem has been solved

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