A and B can separately do a work in 40 days & 30 days . They worked together for 10 days after which B was replaced by C . If the work was finished in next 40/3 days, the number of days in which C alone could do the work?
Question
A and B can separately do a work in 40 days & 30 days . They worked together for 10 days after which B was replaced by C . If the work was finished in next 40/3 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, we need to find the work done by A and B per day. A can complete the work in 40 days, so A's work per day is 1/40. Similarly, B's work per day is 1/30.
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When A and B work together, their combined work per day is 1/40 + 1/30 = 7/240.
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They worked together for 10 days, so the work they completed is 10 * 7/240 = 7/24 of the total work.
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Now, B is replaced by C. The remaining work is 1 - 7/24 = 17/24.
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A and C complete this remaining work in 40/3 days. So, their combined work per day is (17/24) / (40/3) = 17/320.
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We know A's work per day is 1/40, so C's work per day is 17/320 - 1/40 = 1/80.
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Therefore, C alone could do the work in 80 days.
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