Question

The work done by a woman in 8 hours is equal to the work done by a man in 6 hours and by a boy in 12 hours. If working 6 hours per day, 9 men can complete a work in 6 days, then in how many days can 12 men, 12 women and 12 boys together finish the same working 8 hours per day?

• A. \( 2 \frac{1}{2} \) days
• B. \( 1 \frac{1}{2} \) days
• C. \( 3 \frac{1}{2} \) days
• D. None of these

Hint:

Convert all work units to a common standard before solving work efficiency problems.

Answer 1

The Correct Option is B

Let the efficiency of a man be \( M \), a woman be \( W \), and a boy be \( B \).
From the problem: \[ 8W = 6M = 12B \] Solving, we get: \[ W = \frac{3}{4}M, \quad B = \frac{1}{2}M \] Total work = \( 9M \times 6 \times 6 = 324M \).
New group working 8 hours per day: \[ 12M + 12W + 12B = 12M + 9M + 6M = 27M \] Work completed per day: \[ 27M \times 8 = 216M \] Total days required: \[ \frac{324M}{216M} = 1.5 \text{ days} = 1 \frac{1}{2} \text{ days} \] Thus, the answer is \( 1 \frac{1}{2} \) days.