A can do a piece of work in 10 days and B can do the same work in 15 days. If they work together on alternate days starting with A, in how many days will the work be completed?
Explanation:
Total work = LCM(10, 15) = 30 units. Efficiency of A = 3, B = 2. In a 2-day cycle (A then B), work done = 3 + 2 = 5 units. Number of cycles required to complete 30 units = 30 / 5 = 6 cycles. Total days = 6 * 2 = 12 days.
A can finish a work in 15 days and B in 25 days. They start together but B leaves 5 days before the completion of the work. Find the total number of days taken to complete the work.
Explanation:
Total work = LCM(15, 25) = 75 units. Efficiency of A = 5, B = 3. Let total days be x. A works for x days, B works for (x - 5) days. 5x + 3(x - 5) = 75 => 8x - 15 = 75 => 8x = 90 => x = 90/8 = 11.25 days.
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