Question

Four men can do a work in 10 days and 5 women can do the same work in 12 days. How many women must work with 3 men to do the same work in 8 days ?

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

The Correct Option is B

To solve the problem, we'll first find the work done by one man and one woman in one day. Then, we will determine how many women need to work with three men to complete the job in 8 days.

First, observe that 4 men can complete the work in 10 days. Thus, the work done by one man in one day is:

Work by one man in one day = (1 work) / (4 men × 10 days) = 1/40 work.

Similarly, 5 women can complete the work in 12 days. Thus, the work done by one woman in one day is:

Work by one woman in one day = (1 work) / (5 women × 12 days) = 1/60 work.

We are asked to find how many women should work with 3 men to complete the work in 8 days. Let the number of women be 'x'. Then, the work done in one day by 3 men and x women is:

Work by 3 men and x women in one day = 3×(1/40) + x×(1/60).

For the work to be completed in 8 days, the daily work should be:

Work by 3 men and x women in one day = 1/8.

Thus, we set up the equation:

3×(1/40) + x×(1/60) = 1/8.

Simplifying, we get:

3/40 + x/60 = 1/8.

To solve for x, first determine a common denominator (120):

(3/40)×(3/3) = 9/120, and (x/60)×(2/2) = 2x/120.

Substitute these into the equation:

9/120 + 2x/120 = 15/120.

Solving for x:

9 + 2x = 15.

2x = 15 - 9.

2x = 6.

x = 3.

Thus, 3 women must work with 3 men to complete the work in 8 days.

Hence, the correct option is 3.