Working together, A and B can do a job in 6 days. B and C can do the same job in 10 days, while C and A can do it in 7.5 days. How long will it take if all A, B and C work together to complete the job?

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Nitin Sengar

Mathematician

Let total work be 900 units . A + B = 900/6 = 150 unit/day (This is the speed or efficiency of working of A & B together) Similarly , B+C = 90 C + A = 120 adding all three , 2A + 2B + 2C = 360 A + B + C = 180 so A,B & C can do the same job in 900/180 = 5 Days
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If A finishes the work in a days then in one day A does 1/a part of the work. Similarly, B does 1/b and C does 1/c part. IF W is the total work. Then below are per day works W/a + W/b = W/6 W/b + W/c = W/10 W/c + W/a = W/7.5 Adding above equations we get 2(1/a+1/b+1/c) = 1/6+1/10+1/7.5 --- > 1/a + 1/b...
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If A finishes the work in a days then in one day A does 1/a part of the work. Similarly, B does 1/b and C does 1/c part. IF W is the total work. Then below are per day works W/a + W/b = W/6 W/b + W/c = W/10 W/c + W/a = W/7.5 Adding above equations we get 2(1/a+1/b+1/c) = 1/6+1/10+1/7.5 --- > 1/a + 1/b + 1/b = 1/5 all three together do 1/5th of work in a day. So, they take 5 days to finish the work. read less
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