Question

A and B can do a piece of work in 10 days, B and C in 15 days and C and A in 20 days. C alone can do the work in :

• A. 60 days
• B. 80 days
• C. 120 days
• D. 30 days

Answer 1

Answer:

C. 120 days

Total work = LCM (10, 15, 20) = 60 Efficiency of A + B = 60/10 = 6 Efficiency of B + C = 60/15 = 4 Efficiency of C + A = 60/20 = 3 Efficiency of [A + B + B + C + C + A ] = 6 + 4 + 3 = 13 Efficiency of 2[ A + B + C ] = 13 Efficiency of [ A + B + C ] = 13/2 Efficiency of C = Efficiency of [ A + B + C ] - Efficiency of [ A + B ] = 13/2 - 6 = (13 - 12)/6 = 1/6 Time taken by C alone to do the work = 60/(1/6) = 120 days