A group of men decided to do a job in 8 days. But since 10 men dropped out…
2026
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.
150
- B.
165
- C.
175
- D.
80
Attempted by 519 students.
Show answer & explanation
Correct answer: B
Key idea: equate the planned total work to the actual total work after daily dropouts.
Let the initial number of men be N.
Planned total work (if no one dropped out) = N × 8 = 8N man-days.
With 10 men dropping out each day for 12 days, the daily workforce is: N, N−10, N−20, …, N−110.
Actual total work done = sum of those 12 days = 12N − 10 × (1+2+…+11).
Compute the arithmetic series: 1+2+…+11 = 11×12/2 = 66, so actual work = 12N − 10×66 = 12N − 660.
Set planned work equal to actual work: 8N = 12N − 660.
Solve: 4N = 660 ⇒ N = 660 / 4 = 165.
Answer: 165 men were there at the beginning.