Question

A group of men decided to do a job in 8 days. But since 10 men dropped out every day, the job got completed at the end of the 12th day. How many men were there at the beginning?

• A. 165
• B. 175
• C. 80
• D. 90

Hint:

When people drop out daily, model the total work as an arithmetic progression of workers over days.

Answer 1

The Correct Option is A

Step 1: Let initial men = $x$, total work = W. If all worked for 8 days: $x \times 8 = W$. Step 2: With dropouts Day 1: $x$ men, Day 2: $x-10$ men, ..., Day 12: $x-110$ men. Step 3: Total work equation $W = x + (x-10) + (x-20) + \dots + (x - 110)$. This is 12 terms in AP, sum = $\frac{12}{2} [2x - (0 + 110)] = 6(2x - 110) = 12x - 660$. Step 4: Equate $8x = 12x - 660 \Rightarrow 4x = 660 \Rightarrow x = 165$.