Question

8 men can complete a piece of work in 8 days while 8 women can do it in 12 days. In how many days can 2 women and 4 men complete it?

• A. 12 days
• B. 8 days
• C. 17 days
• D. 16 days

Answer 1

Answer:

A. 12 days

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