A can build a wall in 12 days while B can break it in 4 days. A works alone for 6 days, then B joins A and they work together for 3 days. In how many days will A alone finish building the remaining part of the wall?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 12 days.
A's rate of building the wall = 1/12
B's rate of breaking the wall = 1/4
Work done by A alone in 6 days = 6 × (1/12) = 1/2 (Build half of the wall)
Breaking rate of A and B working together = (1/4) - (1/12) = 1/6
Work done in 3 days by A and B together = 3 × (1/6) = 1/2 (Progress is reversed by half)
Total work done after 9 days = 1/2 - 1/2 = 0 (No progress)
Remaining part to build = 1 (full work)
Time taken by A alone to finish the remaining wall = 1/(1/12) = 12 days