A and B can do a work in 12 days and 18 days, respectively. They worked together for 4 days after which B was replaced by C and the remaining work was completed by A and C in the next 4 days. In how many days will C alone complete 50% of the same work?
Question
A and B can do a work in 12 days and 18 days, respectively. They worked together for 4 days after which B was replaced by C and the remaining work was completed by A and C in the next 4 days. In how many days will C alone complete 50% of the same work?
Solution
Sure, let's solve this step by step:
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First, let's find out the one day work of A and B. A can complete the work in 12 days, so A's one day work is 1/12. Similarly, B's one day work is 1/18.
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A and B worked together for 4 days. So, the work done by them in 4 days is 4*(1/12 + 1/18) = 4*(5/36) = 5/9. This means 5/9 of the work has been completed.
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The remaining work is 1 - 5/9 = 4/9.
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This remaining work was completed by A and C in 4 days. So, the combined rate of A and C is (4/9) / 4 = 1/9 per day.
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We know A's one day work is 1/12, so C's one day work is 1/9 - 1/12 = 1/36.
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If C can do 1/36 of the work in one day, then to complete 50% (or 1/2) of the work, C will take (1/2) / (1/36) = 18 days.
So, C alone will complete 50% of the work in 18 days.
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