A group of men decided to do a job in 5 days, but 20 men dropped out every day. Find the number of men who initially decided to do the job, if the job was completed in 7 days?

Let W be the initial number of men and D be the total work. Each day, 20 men drop out, so day n has W - 20(n-1) men. Work done each day: (W-20) + (W-40) + ... + (W-120) = 7W - 420 = 5W (since 5W men would complete it in 5 days). Solving: 7W - 420 = 5W gives W = 210. The arithmetic progression of workers declining by 20 each day is the key insight.