Questions :
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 ?
Options :
- 12 days
- 14 days
- 15 days
- 17 days
correct answer : a)
Explanation :
A can build 1/12 of the wall per day, while B can break 1/4 of the wall per day. In 6 days, A builds 6 × 1/12 = 1/2 of the wall. When A and B work together, their net rate becomes 1/12 − 1/4 = −1/6 wall per day. In 3 days, they complete 3 × (−1/6) = −1/2 wall, which cancels the half wall built earlier. Therefore, after 9 days, no part of the wall remains built. Since A alone can build the entire wall in 12 days, he will need 12 more days to complete the wall. Hence, the correct answer is 12 days.