A and B can do a piece of work in 45 days 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? MCQ with Answer and Explanation
A and B can do a piece of work in 45 days 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?
A. 9 days
B. 12 days
C. 8 days
D. 6 days
Answer: Option A
Solution (By JKSSB Mock Tests)
Total work = LCM(45, 40) = 360 units. Efficiency of A = 8, B = 9. B worked alone for 23 days, so work done = 23 * 9 = 207 units. Remaining work = 360 - 207 = 153 units. This was completed by A and B together. Combined efficiency = 8 + 9 = 17. Time worked together = 153 / 17 = 9 days. Thus, A left after 9 days.
A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days can A alone finish the remaining work?
Explanation:
Total work = LCM(18, 15) = 90 units. Efficiency of A = 5, B = 6. B works for 10 days: work done = 10 * 6 = 60 units. Remaining work = 90 - 60 = 30 units. Time taken by A to finish the remaining work = 30 / 5 = 6 days.
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