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

Solve the same problem using fractions of the whole job instead of picking 24 units, to double check the None of these result.

1. A's daily share: A finishes the whole job in 8 days, so A builds \( \frac{1}{8} \) of the structure each day. In 4 days alone, A builds \( \frac{4}{8} = \frac{1}{2} \) of the structure.
2. Combined daily share for 2 days: B breaks \( \frac{1}{3} \) of the structure each day, so together A and B change the structure by \( \frac{1}{8} - \frac{1}{3} = \frac{3 - 8}{24} = -\frac{5}{24} \) each day. Over 2 days that is \( -\frac{10}{24} = -\frac{5}{12} \).
3. Net structure standing after 6 days: \( \frac{1}{2} - \frac{5}{12} = \frac{6}{12} - \frac{5}{12} = \frac{1}{12} \) of the structure is built.

Remaining work = \(1 - \frac{1}{12} = \frac{11}{12}\). A alone needs \( \frac{11/12}{1/8} = \frac{11}{12} \times 8 = \frac{88}{12} = 7\tfrac{1}{3} \) days, the same result as before.

Let's summarize:

• Since \(7\tfrac{1}{3}\) days does not equal 10, 9, or 12 days, the only option left standing is None of these.

Both the unit-work method and the fraction method agree, confirming option D.