Question

16 workers working 8 hours per day can demolish a building in 32 days. In how many days 24 workers working 12 hours per day can demolish the same building?

• A. 128/3 days
• B. 56/3 days
• C. 128/9 days
• D. 56/9 days

Hint:

To avoid calculation errors, do not multiply the numbers out before dividing.
Keep them in factored form, as shown in Step 3. This allows for quick cancellation and prevents dealing with unnecessarily large numbers during the exam.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This problem involves multiple variables related to work, including the number of workers, the number of hours they work per day, and the number of days they take to complete a task.
We are given a completed scenario of a demolition job and asked to find the time (in days) required to complete the same job under a different configuration of workers and hours.

Step 2: Key Formula or Approach:
We use the work equivalence principle (the MDH formula):
\[ \frac{M_1 \times D_1 \times H_1}{W_1} = \frac{M_2 \times D_2 \times H_2}{W_2} \]
Where:
\(M\) is the number of men (workers).
\(D\) is the number of days.
\(H\) is the number of hours worked per day.
\(W\) is the work done. Since the same building is being demolished in both cases, \(W_1 = W_2\).
Thus, the equation simplifies to:
\[ M_1 \times D_1 \times H_1 = M_2 \times D_2 \times H_2 \]

Step 3: Detailed Explanation:
$\bullet$

Step 1: Identify the given values:
\(M_1 = 16\) workers
\(D_1 = 32\) days
\(H_1 = 8\) hours/day
\(M_2 = 24\) workers
\(H_2 = 12\) hours/day
Let \(D_2\) be the number of days required.
$\bullet$

Step 2: Substitute values into the simplified MDH equation:
\[ 16 \times 32 \times 8 = 24 \times D_2 \times 12 \]
$\bullet$

Step 3: Solve for \(D_2\):
Rearrange the equation:
\[ D_2 = \frac{16 \times 32 \times 8}{24 \times 12} \]
Let's simplify by canceling out common factors:
- Divide 8 in the numerator and 24 in the denominator by 8:
\[ D_2 = \frac{16 \times 32 \times 1}{3 \times 12} \]
- Now, divide 16 and 12 by their common factor of 4:
\[ D_2 = \frac{4 \times 32}{3 \times 3} \]
\[ D_2 = \frac{128}{9} \text{ days} \]

Step 4: Final Answer:
The number of days required by 24 workers working 12 hours per day to demolish the building is 128/9 days.