Question

A can built up a structure in 8 days and B can break it in 3 days. A has worked for 4 days and then B joined to work with A for another 2 days only. In how many days will A alone build up the remaining part of the structure?

• A. 10 days
• B. 9 days
• C. 12 days
• D. None of these

Answer 1

The Correct Option is D

To solve the problem, we need to determine how much of the structure remains after specific workers contribute to the building and destruction of the structure.

Firstly, let's calculate how much work A can do in one day. Since A can build the structure in 8 days, A does 1/8 of the work in one day.

Similarly, B can break the structure in 3 days, meaning B does 1/3 of destruction in one day.

Step-by-step Calculation:

1. A works alone for 4 days:
   • In 4 days, A completes: 4 × (1/8) = 1/2 of the structure.
2. Now, A and B work together for 2 days. A contributes 1/8 per day and B removes 1/3 per day:
   • Net contribution in one day from A and B together: 1/8 - 1/3 = -5/24 (negative indicates destruction).
   • In 2 days, net contribution: 2 × (-5/24) = -10/24 = -5/12.
3. So, total work status after 6 days:
   • Initially A did 1/2 (from 4 days).
   • Then they lost 5/12 (from 2 days together): 1/2 - 5/12 = 1/12 of the structure is left.
4. Now, we need A alone to complete the remaining 1/12:
   • Since A can do 1/8 of the work in a day, to complete 1/12 of the work, A will take: (1/12) / (1/8) = 8/12 = 2/3 days.

Therefore, A alone will take 2/3 days to complete the remaining part of the structure. The correct answer is given as "None of these".