A and B can complete a piece of work in 20 days and 30 days respectively. They work together for some days and then A leaves. If B completes the remaining work in 10 days, for how many days did they work together? MCQ with Answer and Explanation
A and B can complete a piece of work in 20 days and 30 days respectively. They work together for some days and then A leaves. If B completes the remaining work in 10 days, for how many days did they work together?
A. 10 days
B. 12 days
C. 6 days
D. 8 days
Answer: Option D
Solution (By JKSSB Mock Tests)
Total work = LCM(20, 30) = 60 units. Efficiency of A = 3, B = 2. B works alone for 10 days: work completed = 10 * 2 = 20 units. Remaining work = 60 - 20 = 40 units. This was done by A and B together. Combined efficiency = 3 + 2 = 5 units/day. Days worked together = 40 / 5 = 8 days.
Explanation:
Efficiency ratio A : B = 2 : 1. Time ratio A : B = 1 : 2. Difference = 1 part = 20 days. So A takes 20 days and B takes 40 days. Total work = 40 units. Combined efficiency = 3. Time taken together = 40 / 3 = 13(1/3) days.
A and B can do a piece of work in 45 and 40 days respectively. They began the work together, but A left after some days and B finished the remaining work in 23 days. After how many days did A leave?
Explanation:
Total work = LCM(45, 40) = 360 units. Efficiency of A = 8, B = 9. B worked alone for 23 days: work done = 23 * 9 = 207 units. Remaining work = 360 - 207 = 153 units. This was done by A and B together. Combined efficiency = 8 + 9 = 17. Number of days they worked together = 153 / 17 = 9 days. Thus, A left after 9 days.
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