Solution: suppose there are x parts in this batch, and get it according to the meaning of the question.

One-time processing capacity: -20%-X+50.

Processing capacity of B:1/3 ~ x-20% x-50 ~-300 =1/3 ~ 80% x-50 ~-300 = ~ 4/661.

The sum of the quantities processed by Party A and Party B: (20%) x+50+4/15) x-850/3 = (7/15) x-700/.

Processing capacity of C: 3/4 [x-7/15x-700/3]+25 =-2/5-x+200.

∴[﹙7/ 15﹚x-700/3]+[﹙2/5﹚x+200]+ 1300=x

﹙ 13/ 15﹚x- 100/3+ 1300=x

2/ 15x=3800/3

x=9500

This shipment has 9500 parts.