Question

If 1 man or 2 women can finish a job in 20 days, how many days will 3 men and women take to finish the same job?

• A. 3
• B. 5
• C. 6
• D. 4

Hint:

To solve problems involving work and rates, find the combined rate of work by adding the individual rates of the workers.

Answer 1

The Correct Option is D

We are given that 1 man or 2 women can finish a job in 20 days. This implies the work done by 1 man in 1 day is \( \frac{1}{20} \), and the work done by 1 woman in 1 day is \( \frac{1}{40} \) (since 2 women together can finish the job in 20 days, so 1 woman will take 40 days). Now, for 3 men and \( x \) women working together, their combined work per day will be: \[ \text{Work per day} = 3 \times \frac{1}{20} + x \times \frac{1}{40} \] The total work done in 1 day by the group is equal to \( \frac{1}{4} \), so: \[ 3 \times \frac{1}{20} + x \times \frac{1}{40} = \frac{1}{4} \] Solving this equation: \[ \frac{3}{20} + \frac{x}{40} = \frac{1}{4} \] Multiplying through by 40 to eliminate the fractions: \[ 6 + x = 10 \] \[ x = 4 \] Thus, the number of women working is 4, and the total number of workers is 3 men and 4 women. The time required to complete the job will be: \[ \text{Time} = \frac{1}{\text{Work per day}} = \frac{1}{\frac{1}{4}} = 4 \text{ days} \] Thus, the answer is \( 4 \) days.