A, B and C can complete a piece of work in 10, 15 and 20 days respectively. They started together but A left after 2 days and B left 2 days before the completion of the work. Find the total number of days taken to complete the work. MCQ with Answer and Explanation
A, B and C can complete a piece of work in 10, 15 and 20 days respectively. They started together but A left after 2 days and B left 2 days before the completion of the work. Find the total number of days taken to complete the work.
A. 8 days
B. 9 days
C. 7 days
D. 6 days
Answer: Option A
Solution (By JKSSB Mock Tests)
Total work = LCM(10, 15, 20) = 60 units. Efficiency of A = 6, B = 4, C = 3. Let the total work last for x days. A worked for 2 days, so work done = 2 * 6 = 12 units. Remaining work = 60 - 12 = 48 units. B worked for (x - 2) days and C worked for x days. Therefore, 4(x - 2) + 3x = 48 => 4x - 8 + 3x = 48 => 7x = 56 => x = 8 days.
A and B can do a job in 12 days and 16 days respectively. Both work together for 3 days and then A leaves. How long will B take to complete the remaining work?
Explanation:
Total work = LCM(12, 16) = 48 units. Efficiency of A = 4, B = 3. Combined efficiency = 7 units/day. In 3 days, work completed = 7 * 3 = 21 units. Remaining work = 48 - 21 = 27 units. Time taken by B for remaining work = 27 / 3 = 9 days.
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