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Question 99

Three persons A, B and C together complete a work in 3 days; B and C together complete the work in 6 days; and A and C together complete the same work in $$4\frac{1}{2}$$ days. Then the number of days in which C alone can complete the work is

Solution

Let the total work be 18 units and the capacities of A,B,C be a,b,c units/day respectively.
Hence, a+b+c = 6 and b+c = 3 ==> a = 3 units/day
Also, a + c = 4 hence, c = 1 unit/day.
Hence, time required by C alone to complete all the work = 18 days

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