A, B and C can do a work separately in 24, 36 and 48 days respectively. B leaves 7 days before completion and A left 3 days before completion. work will finish in how many days?Options11 5/1312 7/1314 8/1313 9/13
Question
A, B and C can do a work separately in 24, 36 and 48 days respectively. B leaves 7 days before completion and A left 3 days before completion. work will finish in how many days?Options11 5/1312 7/1314 8/1313 9/13
Solution
To solve this problem, we first need to find the rate at which A, B, and C work.
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A's work rate is 1/24 of the work per day, B's work rate is 1/36 of the work per day, and C's work rate is 1/48 of the work per day.
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The combined work rate of A, B, and C is (1/24 + 1/36 + 1/48) = 1/8 of the work per day.
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If B leaves 7 days before completion and A leaves 3 days before completion, then for the last 7 days, only C is working, and for the 3 days before that, both A and C are working.
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In the last 7 days, C completes 7 * (1/48) = 7/48 of the work.
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In the 3 days before that, A and C together complete 3 * (1/24 + 1/48) = 1/8 of the work.
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The remaining work to be done is 1 - (7/48 + 1/8) = 5/8 of the work.
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At the combined work rate of A, B, and C, this remaining work will take (5/8) / (1/8) = 5 days.
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Therefore, the total time taken to complete the work is 5 days (for A, B, and C together) + 3 days (for A and C) + 7 days (for C) = 15 days.
So, the work will be finished in 15 days. None of the options provided match this answer.
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