:Q BUSINESS PROBLEMS 1. A dealer reduces his profit from 33 1/3% to 25%. How much less would you pay for an article that cost the dealer $30.00? (a) $5.00 (b) $24.00 (c) $2.50 (d) $2.00 (e) $2.20 :RCC 1. (c) $2.50 Ans. Savings = former profit - present profit % profit amt. profit -------- = ------------- 100 original cost 33 1/3 y 25 y ------ = -- --- = -- 100 30 100 30 100y = 1000 100y = 750 y = $10.00 y = $7.50 Savings = $2.50 Ans. :RA Strategy: (33 1/3% of $30) - (25% of $30) :RA :Q 2. A dealer makes 25% profit. If he sells an article for $5.00, what does it cost him? (a) $8.00 (b) $9.00 (c) $10.00 (d) $4.00 (e) $4.25 :RCD 2. (d) $4.00 Ans. % profit amt. profit -------- = ------------- 100 original cost 25 5 - y --- = ----- 100 y 100(5 - y) = 25y 500 - 100y = 25y 500 = 125y 4 = y cost Ans. :RA :Q 3. An article costs a dealer n dollars. At what price must he sell in order to make a 30% profit on the selling price? (a) 13n/$10 (b) 10$n (c) 7n/$10 (d) 100n/$7 (e) 7n/$100 :RCA 3. (a) 13n/$10 Ans. % profit amt. profit -------- = ------------- 100 original cost 30 y --- = - 100 n 100y = 30n y = 3n/10 profit :RA cost + profit = selling price n + 3n/10 = selling price 10n + 3n -------- = selling price 10 13n --- = selling price Ans. 10 :RA :Q 4. A dealer reduces his prices by 20%. When sales pick up, he raises his prices 20%. What is the net change? (a) 3% (b) 6% (c) 0% (d) 4% (e) 5% :RCD 4. (d) 4% Ans. let y = original price .8y = reduced price (.8y)(1.2) = final price .96y = final price final price = 96% of original price net change = 4% reduction Ans. Note: An increase of 20% makes the new price 120% = 1.2 times the former price. :RA :Q 5. A company makes n% profit on an article costing d dollars. Find the selling price. 100d + dn 200d + dn (a) --------- (b) --------- 100 100 (c) 100d + dn (d) 100dn + d 100dn + n (e) --------- 100 :RCA 100d + dn 5. (a) --------- Ans. 100 n Selling price = y = d + d x --- 100 100y = 100d + dn 100d + dn y = --------- Ans. 100 :RA :Q WORK PROBLEMS 1. Tom, Dick and Harry can do a certain job in 1 hour and 20 minutes when working together. Working alone, Tom can do the same job in 3 hours and Dick can do it in 4 hours. How many hours would it take Harry to do the job alone? (a) 4 hrs. (b) 3 hrs. (c) 8 hrs. (d) 12 hrs. (e) 6 hrs. :RCE 1. (e) 6 hrs. Ans. Let y = hours for Harry to do job alone part by Tom in 1 hr. + part by Dick in 1 hr. + part by Harry in 1 hr. = part by all 3 in 1 hr. 1 1 1 1 - + - + - = - 3 4 y 4 - 3 :RA Simplify to: 1 1 1 3 - + - + - = - 3 4 y 4 Multiply by 12y: 4y + 3y + 12 = 9y Solve for y: 12 = 2y 6 = y hrs. Ans. :RA :Q 2. A swimming pool has two inlet pipes which can fill it in 6 hours and 12 hours, respectively. When the outlet pipe was left open by mistake, it took 8 hours for both inlet pipes to fill the pool. How many hours does it take the outlet pipe to drain the pool? (a) 7 hrs. (b) 4 hrs. (c) 1 hrs. (d) 8 hrs. (e) 0 hrs. :RCD 2. (d) 8 hrs. Ans. Let y = hrs. for outlet pipe to drain Let A represent the larger inlet pipe, B the smaller inlet pipe, and C the outlet pipe. Then: part by A in 1 hr + part by B in 1 hr - part by C in 1 hr = part by all in 1 hr. 1 1 1 1 - + - - - = - 6 12 y 8 :RA Multiply by 24y: 4y + 2y - 24 = 3y Solve for y: 3y = 24 y = 8 hrs. Ans. :RA :Q 3. Mr. Smith can finish Rubick's Cube in half the time it takes his son Kenneth. After working together for 3 hours, Mr. Smith leaves, and Kenneth finishes the job in 1 hour. How many hours would it take Kenneth to finish the cube alone? (a) 5 hrs. (b) 4 hrs. (c) 10 hrs. (d) 15 hrs. (e) 20 hrs. :RCC 3. (c) 10 hrs. Ans. Let y = hours for Mr. Smith alone to do the job. Let 2y = hours for Kenneth alone to do the job. part by Mr. Smith in 3 hrs + part by Kenneth in 4 hrs = part by both 3 4 - + -- = 1 y 2y Multiply by 2y: 6 + 4 = 2y 2y = 10 hrs. Ans. :ET :ET Copyright ARROW INSTRUCTIONAL SYSTEMS July 1983
