A and B can do a piece of work in 10 days and 15 days respectively. They work together for 2 days and then A is replaced by C. The work is finished in next 4 days. In how many days can C alone finish the work? MCQ with Answer and Explanation

Total work = LCM(10, 15) = 30 units. Efficiency of A = 3, B = 2. In 2 days, A and B do 2 * (3 + 2) = 10 units. Remaining work = 30 - 10 = 20 units. This is completed by B and C in 4 days, so combined efficiency of B and C = 20 / 4 = 5 units/day. Since efficiency of B = 2, efficiency of C = 5 - 2 = 3 units/day. Time taken by C alone = 30 / 3 = 10 days.