Tutorial Week 2
Quantitative Methods for Business
Tutorial Week 2
(Percentages, Ratios and Proportions)
Please note: You should review the relevant lecture notes and sections in the textbook and attempt the questions before coming to the tutorial. Bring a calculator (not one on your mobile phone!).
Exercises:
1. A store sells washing machines for a retail price of $1000 (including GST). To clear out stock in preparation for the new model, the store marks these down by 25%. A customer comes into the store and agrees to buy a discounted machine, only if a further 10% discount is given for paying cash.
(a) How much in cash is the customer willing to pay?
(b) The store says it will not give a further discount of 10% for cash, but will give the customer a total discount of 35% off the original retail price. Is the customer better or worse off with this deal? Explain.
2. New! Three friends, Geoff, Brooke and Longyuan, form a business partnership in which Geoff invests $50 000, Brooke $30 000 and Longyuan $20 000. Brooke and Longyuan are each to receive a fixed sum of $20 000 out of the profit, and the remaining profit is to be shared among the three partners in proportion to their investment.
(a) After the $40 000 in salaries have been paid, what percentage of the remaining profit is received by Geoff?
(b) Calculate the total profit shares of each of the three partners if the total partnership profit is $120 000.
(c) If Geoff receives $95 000, what is the total partnership profit?
3. Stan is a real estate salesperson. He receives 60% of 5% commission that the real estate agency charges on sales. If his income for the past year was $84,000, what was his dollar volume of sales for the year?
4. A test-marketing of a newly released product in a representative Australian town, with a population of 120,000, resulted in sales of 543 units in a 3-month period. If the product sells at the same rate in the rest of the country, where 21,000,000 people have access to retail outlets, what
Tutorial Week 2
(Percentages, Ratios and Proportions)
Please note: You should review the relevant lecture notes and sections in the textbook and attempt the questions before coming to the tutorial. Bring a calculator (not one on your mobile phone!).
Exercises:
1. A store sells washing machines for a retail price of $1000 (including GST). To clear out stock in preparation for the new model, the store marks these down by 25%. A customer comes into the store and agrees to buy a discounted machine, only if a further 10% discount is given for paying cash.
(a) How much in cash is the customer willing to pay?
(b) The store says it will not give a further discount of 10% for cash, but will give the customer a total discount of 35% off the original retail price. Is the customer better or worse off with this deal? Explain.
2. New! Three friends, Geoff, Brooke and Longyuan, form a business partnership in which Geoff invests $50 000, Brooke $30 000 and Longyuan $20 000. Brooke and Longyuan are each to receive a fixed sum of $20 000 out of the profit, and the remaining profit is to be shared among the three partners in proportion to their investment.
(a) After the $40 000 in salaries have been paid, what percentage of the remaining profit is received by Geoff?
(b) Calculate the total profit shares of each of the three partners if the total partnership profit is $120 000.
(c) If Geoff receives $95 000, what is the total partnership profit?
3. Stan is a real estate salesperson. He receives 60% of 5% commission that the real estate agency charges on sales. If his income for the past year was $84,000, what was his dollar volume of sales for the year?
4. A test-marketing of a newly released product in a representative Australian town, with a population of 120,000, resulted in sales of 543 units in a 3-month period. If the product sells at the same rate in the rest of the country, where 21,000,000 people have access to retail outlets, what