Problem -11: A storekeeper has read that a 42% markup from wholesales is common,

Question

Problem -11: A storekeeper has read that a 42% markup from wholesales is common, and tickets all her merchandise accordingly. But business is not too good. She decided that she can manage to do ok with a 35% markup. So, she decides to run a one-month sale. [ round all answers to the nearest tenth] [5 points] a) What percent discount should she offer, to end up with a 355 profit? Illustrate your answer with a fancy TV she paid $800 for. b) What was the original selling price she put on the ticket? c) Show how the %-off sale reduced the price to a new, sale price. d) What percent discount did the buyer get? e) Did the storekeeper really end up making the 35% profit?

Explanation / Answer

a)

42% markup means, a product costing 100 would cost = 100 + 42%*100 = 142

35% markup = 100 + 35%*100 = 135

discount needed to bring from 42% to 35% = 142 - 135 = 7

discount % needed = 7/142 = 0.0493 = 4.92%

b)

cost price = 800

original selling is with 42% markup = 800 + 42%*800 = 1136

c)

we need 35% markup: hence we give a discount of 4.92% = 1136 - 1136*4.92% = 1136 - 55.89 = 1080.11

new price = 1080.11

markup = 1080.11 - 800 = 280.11

% markup = 280.11/800 = 0.3501 = 35.01%

c)

When giving a discount, 4.92% doesn't provide a good impression to the customer, hence rounding off to nearest whole number = 5%

Hence discount received by customer = 5%

d)

actual discounted price = 1136 - 1136*5% = 1079.2

hence actual profit = 1079.2 - 800 = 279.2

profit % = 279.2/800 = 34.9%

Hence no, the shopkeeper did not receive 35% profit, it received 34.9%

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