'A' can build up a structure in 8 days and 'B' can break it in 3 days. 'A' worked building for 4 days and then 'B' joined and start breaking while 'A' kept building for another 2 days. In how many days will 'A' alone build up the remaining part of the structure?

$\frac{22}{3}$ days

The correct answer is Option (4) → $\frac{22}{3}$ days

Let the whole structure = 1 unit

Given rates

• A can build in 8 days → A’s rate = $\frac{1}{8}$​ per day
• B can break in 3 days → B’s rate = $\frac{1}{3}$​ per day (breaking)

Step 1: Work done by A in first 4 days

$4 \times \frac{1}{8} = \frac{1}{2}$​

Step 2: Next 2 days (A builds, B breaks)

Net rate:

$\frac{1}{8} - \frac{1}{3} = \frac{3 - 8}{24} = -\frac{5}{24}$

Work undone in 2 days:

$2 \times \left(-\frac{5}{24}\right) = -\frac{5}{12}$

Remaining work after 6 days:

$\frac{1}{2} - \frac{5}{12} = \frac{6 - 5}{12} = \frac{1}{12}$

Step 3: Remaining part to be built

$1 - \frac{1}{12} = \frac{11}{12}$

Step 4: Time taken by A alone to complete remaining work

$\frac{11}{12} \div \frac{1}{8} = \frac{11}{12} \times 8 = \frac{88}{12} = \frac{22}{3}$