A can build up a wall in 8 days while B can break it in 3 days. A has worked for 4 days and then B joined to work with A for anot…

Question

A can build up a wall in 8 days while 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 wall?

1. A. \(713\) days (Correct answer)
2. B. \(825\) days
3. C. \(915\) days
4. D. \(512\) days

Correct Answer

Option A — \(713\) days

Detailed Solution & Explanation

The correct answer is 7⅓ days.

Key Points

• A builds at 1/8 per day; B destroys at 1/3 per day, so B's contribution is −1/3.
• A works alone for 4 days: 4 × 1/8 = 1/2 of the wall built.
• A and B together for 2 days: 2 × (1/8 − 1/3) = 2 × (−5/24) = −5/12.
• Wall standing after 6 days = 1/2 − 5/12 = 1/12, so 11/12 remains to be built.
• A alone needs (11/12) ÷ (1/8) = 88/12 = 22/3 = 7⅓ days.

Additional Information

• Destructive work carries a negative rate; the same treatment applies to a leaking pipe emptying a cistern while inlet pipes fill it.
• B is more than twice as fast at breaking as A is at building, so their combined effort is net negative — the wall shrinks during those two days, which is the point of the question.
• Note the phrasing "the remaining part of the wall": the answer is the time to build the outstanding 11/12, not the whole wall over again.

प्रश्न (हिन्दी में)

A एक दीवार को 8 दिन में बना सकता है जबकि B इसे 3 दिन में तोड़ सकता है। A ने 4 दिन काम किया और फिर B ने A के साथ मिलकर केवल 2 दिन और काम किया। A अकेले दीवार का बचा हुआ हिस्सा कितने दिन में बना लेगा?

1. A. \(713\) दिन
2. B. \(825\) दिन
3. C. \(915\) दिन
4. D. \(512\) दिन