A can do a piece of work in 40 days. He works at it for 8 days and then B finishes it in 16 days. How long will A and B together take to complete the work? MCQ with Answer and Explanation
A can do a piece of work in 40 days. He works at it for 8 days and then B finishes it in 16 days. How long will A and B together take to complete the work?
A. 25 days
B. 20 days
C. 13(1/3) days
D. 15 days
Answer: Option C
Solution (By JKSSB Mock Tests)
Let total work be 40 units. Efficiency of A = 1 unit/day. In 8 days, A completes 8 units. Remaining work = 40 - 8 = 32 units. B finishes 32 units in 16 days, so B's efficiency = 32 / 16 = 2 units/day. Combined efficiency of A and B = 1 + 2 = 3 units/day. Time taken together = 40 / 3 = 13(1/3) days.
A can do a piece of work in 12 days and B can do the same work in 18 days. They work together for 4 days and then A leaves. How many days will B take to complete the remaining work?
Explanation:
Total work = LCM(12, 18) = 36 units. Efficiency of A = 3, B = 2. Combined efficiency = 5. In 4 days, work completed = 4 * 5 = 20 units. Remaining work = 36 - 20 = 16 units. Time taken by B to complete the remaining work = 16 / 2 = 8 days.
A can finish a work in 10 days and B in 15 days. B starts the work and is joined by A after 5 days. What is the total number of days taken to complete the work?
Explanation:
Total work = LCM(10, 15) = 30 units. Efficiency of A = 3, B = 2. B works alone for 5 days: work completed = 5 * 2 = 10 units. Remaining work = 30 - 10 = 20 units. Now A and B work together with efficiency = 3 + 2 = 5 units/day. Time taken for remaining work = 20 / 5 = 4 days. Total time = 5 + 4 = 9 days.
A can complete a piece of work in 12 days, while B can complete the same work in 15 days. If they work together, how many days will they take to complete the work?
Explanation:
Let the total work be the LCM of 12 and 15, which is 60 units. Efficiency of A = 60 / 12 = 5 units/day. Efficiency of B = 60 / 15 = 4 units/day. Combined efficiency of A and B = 5 + 4 = 9 units/day. Time taken together = 60 / 9 = 20 / 3 = 6(2/3) days.
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