A logistics company has three branches: Bukhara with 20 employees, Navoi with 30 and Samarkand with 40. This year the head office set aside 36,000 dollars for staff training.
The first idea was to give each branch 12,000 dollars. The Samarkand manager objected: his branch had twice as many people as Bukhara, so an equal split would give each of his employees half as much training. The director agreed that money should be shared in proportion to the number of staff.
The staff numbers 20, 30 and 40 are in the ratio 2 to 3 to 4, which makes nine parts in total. The director divided 36,000 by nine and got 4,000 dollars per part. Bukhara received two parts, or 8,000 dollars. Navoi received three parts, or 12,000. Samarkand received four parts, or 16,000.
The chief accountant checked the split in a second way. The company has 90 employees, and 36,000 dollars for 90 people is 400 dollars per person. Twenty people at 400 dollars is 8,000, thirty is 12,000 and forty is 16,000. Both methods gave the same answer, and the three amounts added up to 36,000.
The Navoi manager noticed something interesting: his branch received exactly the same amount as under the first, equal plan. The change had only moved money from Bukhara to Samarkand. "A fair split," the director said, "is not always an equal one."