A and B can complete a work in 6 days.A can alone do it in 10 days.Then B can alone do the work in how many days?A13.75 daysB14 daysC16 daysD15 days
Question
A and B can complete a work in 6 days.A can alone do it in 10 days.Then B can alone do the work in how many days?A13.75 daysB14 daysC16 daysD15 days
Solution
To solve this problem, we need to understand the concept of work and rate.
Step 1: Find the rates of A and B working together. Since A and B can complete the work in 6 days, their combined rate is 1 work/6 days = 1/6 work per day.
Step 2: Find the rate of A working alone. Since A can complete the work alone in 10 days, A's rate is 1 work/10 days = 1/10 work per day.
Step 3: Find the rate of B working alone. We know that the combined rate of A and B is the sum of their individual rates. So, we can find B's rate by subtracting A's rate from their combined rate. B's rate = (A and B's rate) - A's rate = (1/6 - 1/10) work per day = 1/15 work per day.
Step 4: Find the time it takes for B to complete the work alone. Since rate is work/time, we can find the time by dividing the work by the rate. Time = Work/Rate = 1 work / (1/15 work per day) = 15 days.
So, B can alone do the work in 15 days. The answer is D. 15 days.
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