BUSINESS PROBLEMS Business problems involve percents. A sum of money (used as a base) multiplied by a percent (rate) gives a percentage, which may be either profit, loss, discount, commission, etc. Note: base x rate = percentage You should distinguish clearly between a profit, which is an amount of money, and a percent profit, which is merely a rate. :RA Other formulas frequently used are: 1. cost + gain = selling price 2. cost - loss = selling price 3. list price - disc. = selling price. If there is no indication to the contrary, profit or loss is assumed to be based on cost. :RA WORK PROBLEMS The basic relationship in problems of this type involves the part (fraction) of the work done in a given time since the whole job always equals the sum of the parts done by the individual workers. The nature of the work does not matter since a job may be considered a unit, that is 1. If a person can do a job in 4 hours, he will do 1/4 of the job in 1 hour; 3/4 of the job in 3 hours; and n/4 part of the job in n hours. If a job can be done in y days, then 1/y part of it can be done in 1 day; 2/y of it in 2 days; and n/y of it in y days. :RA TYPE 1. You are given the time needed for each of several workers to do a job alone. You are required to find the time it would take the workers to do the job together. :RA Example: A school newspaper can be printed on a new printing press in 4 hours and by an old one in 6 hours. How long would it take both presses to print the newspaper if they operate together? Let y = hours for both presses to print the newspaper. part done by new press in 1 hr. + part by old press in 1 hr. = part by both in 1 hr. 1 1 1 - + - = - 4 6 y :RA Multiply by 12y: 3y + 2y = 12 Solve for y: 5y = 12 y = 12/5 = 2 2/5 y = 2.4 hours Ans. :RA TYPE 2. You are given the time it takes several workers to do a job together. You are to find the time it would take a worker to do the job alone. :RA Example: Larry and Barb together can type the stencils for their class newspaper in 4 hours. Larry can type them alone in 6 hours. How long does it take Barb alone to cut the stencils? Let y = hours for Barb alone. part by Larry in 1 hr. + part by Barb in 1 hr. = part by both in 1 hr. 1 1 1 - + - = - 6 y 4 Multiply by 12y: 2y + 12 = 3y Solve for y: y = 12 hr. Ans. :RA TYPE 3. A job (or amount of work) is considered to be inversely proportional to the number of persons doing the job. If 6 men can do a job in 4 hours. The same job can be done by 8 men in 3 hours. The more men on the job the less time it takes. :RA Example: If 16 men pave a highway in 6 days, how long would it take a crew of 24 men to do the same job? INVERSE PROPORTION men days 16 y -- = - 24 6 24y = 96 y = 4 days Ans. :ET :ET Copyright ARROW INSTRUCTIONAL SYSTEMS July 1983 6 24y = 96 y = 4 days Ans. :ET :ET Copyright ARROW INSTRUCTIONAL SYSTEMS July
