A can complete a work in 24 days and B can complete the same work in 24 days. If they work together, in how many days will the work be completed? MCQ with Answer and Explanation

Explanation:
Total work = LCM(12, 15, 20) = 60 units. Efficiency of (A+B) = 5, (B+C) = 4, (C+A) = 3. Summing these gives 2*(A+B+C) = 12 => Efficiency of (A+B+C) = 6. Efficiency of A = (A+B+C) - (B+C) = 6 - 4 = 2. Time taken by A alone = 60 / 2 = 30 days.

Explanation:
Combined rate = 1/19 + 1/19. Time = 9.5 days.

Explanation:
Let efficiency of C = 1. Then efficiency of B = 3 * 1 = 3. Efficiency of A = 2 * 3 = 6. Total work = Efficiency of C * Time of C = 1 * 24 = 24 units. Combined efficiency of A, B and C = 6 + 3 + 1 = 10. Time taken together = 24 / 10 = 2.4 days.