Enigma 1151: Workers’ bonus
5 September 2016
Posted by on
From New Scientist #2307, 8th September 2001 [link]
Each of the workers of the Manufacturing Company joined the company on 30 June in some year before 1996. The company’s profits for each year ending 30 June are always the same, £P, where P is a whole number between 2000 and 2500. On the 30 June each year, each worker, W, receives a bonus of P × (A/B) pounds, rounded, if necessary, to the nearest pound, with 50p going up; where A = the number of years W has worked for the company, and B = the sum of the numbers of years worked for the company by all the workers. Worker Frances found that in each of the years 1996, 1997 and 1998 her figure P × (A/B) was a whole number and she received bonuses of £315, £336 and £350, respectively.
Question 1. What is P?
Frances joined the company at least one year later than every other worker. Suppose that all the workers live for 1000 years and over that 1000 years the company’s annual profits remain at £P and no worker joins or leaves the company.
Question 2. What is the first year when all the workers will receive the same bonus?