Question

Four men can do 60% of a work in 6 days, whereas 6 women can do 50% of the same work in 5 days. How many days will 2 men and 3 women take to do the work if they work together?

• A. 9
• B. \(9\frac{1}{2}\)
• C. 10
• D. 12

Hint:

Find per day work of one person first

Answer 1

The Correct Option is C

Step 1: Find time for 4 men to complete 100% work.
4 men do 60% in 6 days.
4 men do 100% in \(6 \times \frac{100}{60} = 6 \times \frac{5}{3} = 10\) days.
So 4 men complete work in 10 days. Step 2: Find 1 man's 1-day work.
1 man's 1-day work = \(\frac{1}{4 \times 10} = \frac{1}{40}\). Step 3: Find time for 6 women to complete 100% work.
6 women do 50% in 5 days.
6 women do 100% in \(5 \times \frac{100}{50} = 5 \times 2 = 10\) days.
So 6 women complete work in 10 days. Step 4: Find 1 woman's 1-day work.
1 woman's 1-day work = \(\frac{1}{6 \times 10} = \frac{1}{60}\). Step 5: Find combined 1-day work of 2 men and 3 women.
2 men's work = \(2 \times \frac{1}{40} = \frac{1}{20}\).
3 women's work = \(3 \times \frac{1}{60} = \frac{1}{20}\).
Total = \(\frac{1}{20} + \frac{1}{20} = \frac{2}{20} = \frac{1}{10}\). Step 6: Find number of days.
Days = \(1 \div \frac{1}{10} = 10\) days.