A can do a certain work in same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in how many days?20 days24 days25 days30 days
Question
A can do a certain work in same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in how many days?20 days24 days25 days30 days
Solution
To solve this problem, we first need to understand that the rate of work done is inversely proportional to the time taken to complete the work.
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Let's denote the rates at which A, B, and C work as a, b, and c respectively. From the problem, we know that A can do the work in the same time as B and C together, so a = b + c.
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We also know that A and B together can do the work in 10 days, so a + b = 1/10.
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And we know that C can do the work alone in 50 days, so c = 1/50.
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Now we can substitute a = b + c into the second equation to get b + c + b = 1/10, which simplifies to 2b + 1/50 = 1/10.
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Solving this equation for b, we find that b = 1/20 - 1/100 = 1/25.
So, B alone could do the work in 25 days. The correct answer is 25 days.
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