Question

8 men can finish a piece of work in 8 days, whereas it takes 10 women to finish it in 8 days. If 12 men and 5 women undertook to complete the work, then how many days will they take to complete it?

• A. 2 Days
• B. 3 Days
• C. 4 Days
• D. 5 Days

Answer 1

The Correct Option is C

Finding the Number of Days Required to Complete the Work 

Step 1: Define Total Work

Let the total work be \( W \).

Step 2: Compute Work Done Per Day

• Work done by 8 men in 8 days = \( W \), so 1 man’s 1-day work is: \[ \frac{W}{8 \times 8} = \frac{W}{64} \]
• Work done by 10 women in 8 days = \( W \), so 1 woman’s 1-day work is: \[ \frac{W}{10 \times 8} = \frac{W}{80} \]

Step 3: Compute Work Done by 12 Men and 5 Women Per Day

Work done per day by 12 men: \[ 12 \times \frac{W}{64} = \frac{12W}{64} = \frac{3W}{16} \]

Work done per day by 5 women: \[ 5 \times \frac{W}{80} = \frac{5W}{80} = \frac{W}{16} \]

Total work done per day: \[ \frac{3W}{16} + \frac{W}{16} = \frac{4W}{16} = \frac{W}{4} \]

Step 4: Compute the Required Number of Days

Days required to complete \( W \) work:

\[ \frac{W}{W/4} = 4 \text{ days} \]

Final Answer:

Thus, the correct answer is 4 days (Option C).