A and B can separately do a work in 12 days & 24 days . They worked together for 6 days after which B was replaced by C . If the work was finished in next 9/4 days, the number of days in which C alone could do the work?
Question
A and B can separately do a work in 12 days & 24 days . They worked together for 6 days after which B was replaced by C . If the work was finished in next 9/4 days, the number of days in which C alone could do the work?
Solution
Sure, let's solve this step by step:
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First, let's find out the work done by A and B in one day. Since A can complete the work in 12 days, A can do 1/12 of the work in one day. Similarly, since B can complete the work in 24 days, B can do 1/24 of the work in one day.
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When A and B work together, they can do (1/12 + 1/24) of the work in one day. This simplifies to 1/8 of the work in one day.
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They worked together for 6 days, so in 6 days they completed 6 * (1/8) = 3/4 of the work.
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Now, B is replaced by C. The remaining work is 1 - 3/4 = 1/4.
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This remaining work is completed in 9/4 days. So, C can do 1/4 of the work in 9/4 days.
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Therefore, the number of days in which C alone could do the work is (9/4) * 4 = 9 days.
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