A can build a wall in 30 days, while B can destroy it in 40 days. If they work on alternate days starting with A, in how many days will the wall be built? MCQ with Answer and Explanation
A can build a wall in 30 days, while B can destroy it in 40 days. If they work on alternate days starting with A, in how many days will the wall be built?
A. 233 days
B. 240 days
C. 235 days
D. 237 days
Answer: Option A
Solution (By JKSSB Mock Tests)
Total work = LCM(30, 40) = 120 units. Efficiency of A = +4, B = -3. In 2 days, net work = 4 - 3 = 1 unit. We look for when the work reaches 120 - 4 = 116 units. 116 units are done in 116 * 2 = 232 days. On the 233rd day, A works and completes 4 units, making total work 116 + 4 = 120 units. Thus, the wall is completed in 233 days.
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?
Explanation:
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 and B can complete a work 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 = 3 * 7 = 21 units. Remaining work = 48 - 21 = 27 units. Time taken by B to complete remaining work = 27 / 3 = 9 days.
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