Days taken by 3 men and 4 women to finish the job

Step 1: Establish the relationship between men and women's work rate

Given that 1 man can finish a job in 20 days and 2 women can also finish the same job in 20 days,
we can deduce the work equivalence between men and women.

1 man = 2 women

Step 2: Convert the workforce to a single unit (women)

We need to find out how many days 3 men and 4 women will take to finish the job.
Let's convert the men into an equivalent number of women:

3 men = 3 × 2 women = 6 women

Total workforce = 6 women + 4 women = 10 women

Step 3: Calculate the work rate of one woman

If 2 women can finish the job in 20 days, then the total "woman-days" required to complete the job is:

2 women × 20 days = 40 woman-days

This means one woman would take 40 days to complete the job alone.

Step 4: Calculate the time taken by the combined workforce

Now, we can find out how many days 10 women will take to finish the job:

Days = Total woman-days ÷ Number of women = 40 ÷ 10 = 4 days

Answer:

The correct answer is (D) 4.