4 A and B can do a piece of work in 8 days, B and C can do it in 24 days, while C and A can do it in 87 days. In how many days can C do it alone?

Explanation

60 Let total work = L.C.M. (8,24, 7 ) = 120 units Let efficiencies of A, B and C are a, b and c respectively. 120 A and B can do the piece of work in 8 days = a + b = 8 = 15 units/day----------(i) 120 Similarly, b + c = 24 = 5 units/day----------- (ii) 16200 And c + a = 7 = 14 units/day-----------(iii) Adding the three equations, we get : => 2(a + b + c) = 15 + 5 + 14 34 => (a + b + c) = 2 = 17 Substituting value of a + b from equation (i) in above equation, => 15 + c = 17 => c = 17 − 15 = 2 units/day 120 ∴ Time taken by C alone to finish the work = 2 = 60 days