A12 days
B8 days
C17 days
D16 days
Answer:
A. 12 days
Read Explanation:
Concept:
The amount of work done is proportional to the number of people, the rate at which they work, and the time they spend.
Work = Rate × Time × Number of People.
Men's Work Rate:
8 men complete a work in 8 days.
This means 1 man's work rate is 1 / (8 men × 8 days) = 1/64 of the total work per day.
So, in one day, 1 man does 1/64 of the work.
Women's Work Rate:
8 women complete the same work in 12 days.
This means 1 woman's work rate is 1 / (8 women × 12 days) = 1/96 of the total work per day.
So, in one day, 1 woman does 1/96 of the work.
Calculating Combined Work Rate
Combined Rate of 4 Men and 2 Women per Day:
The work done by 4 men in one day = 4 × (1/64) = 4/64 = 1/16 of the total work.
The work done by 2 women in one day = 2 × (1/96) = 2/96 = 1/48 of the total work.
The total work done by 4 men and 2 women in one day = (1/16) + (1/48).
To add these fractions, find a common denominator, which is 48.
(1/16) + (1/48) = (3/48) + (1/48) = 4/48 = 1/12 of the total work per day.
Determining the Time to Complete the Work
Calculation:
If 4 men and 2 women together complete 1/12 of the work in one day, they will complete the entire work (1 whole) in the reciprocal of this rate.
Time = Total Work / Combined Daily Rate
Time = 1 / (1/12) = 12 days