Question

A can build up a structure in 8 days and B can break it down in 3 days. A worked alone for 4 days, 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

Hint:

Treat B's work as negative since B breaks down what A builds, then find how much of the structure actually stands after 6 days.

Answer 1

The Correct Option is D

Step 1: Pick a convenient total work value.
Let the total structure be 24 units, the LCM of 8 and 3, so A's building rate is \( \frac{24}{8} = 3 \) units a day, and B's breaking rate is \( \frac{24}{3} = 8 \) units a day, counted as \(-8\) since B destroys work.

Step 2: Find the work done by A alone in the first 4 days. \[ 4 \times 3 = 12 \text{ units built} \]

Step 3: Find the net work when A and B work together for 2 days.
Combined daily rate = \(3 - 8 = -5\) units a day, so in 2 days: \[ 2 \times (-5) = -10 \text{ units} \]

Step 4: Find total work standing after 6 days. \[ 12 + (-10) = 2 \text{ units built so far} \]

Step 5: Find the work still remaining and the days A alone needs.
Remaining work = \(24 - 2 = 22\) units. A alone builds at 3 units a day, so days needed = \[ \frac{22}{3} = 7\tfrac{1}{3} \text{ days} \]

Step 6: Compare with the given options.
\(7\tfrac{1}{3}\) days matches none of 10, 9, or 12 days exactly, so options A, B and C are all wrong.

Final Answer:
Since the exact time is \(7\tfrac{1}{3}\) days, which is not listed, the correct choice is None of these. \[ \boxed{\text{None of these}} \]