A corner shop buys a stock item at a wholesale cost of \(\pounds C\). The shop marks up the price by \(60\%\) to set the retail price. During a clearance sa...
Question 1 Report
A corner shop buys a stock item at a wholesale cost of \(\pounds C\). The shop marks up the price by \(60\%\) to set the retail price. During a clearance sale, the retail price is then reduced by \(25\%\), giving a sale price of \(\pounds 54\).
- Form a single equation, in terms of \(C\), for the sale price. (2)
- Solve your equation to find \(C\). (2)
- Work out the shop's profit, in pounds, made by selling at \(\pounds 54\) compared with the wholesale cost. (1)
- Express this profit as a percentage of the wholesale cost. (2)
Answer Details
A markup and a subsequent discount both act as multipliers on the price; combining the wholesale-to-retail markup with the sale discount into a single multiplier links the wholesale cost directly to the final sale price in one equation.
(a) A \(60\%\) markup gives a multiplier of \(1.6\); a \(25\%\) reduction gives a multiplier of \(0.75\). Applying both to the wholesale cost: \(C\times1.6\times0.75=54\), which combines to \(1.2C=54\). [2 marks]
(b) Dividing both sides by \(1.2\): \(C=54\div1.2=\pounds45\). [2 marks]
(c) Profit is the sale price minus the wholesale cost: \(54-45=\pounds9\). [1 mark]
(d) Percentage profit is the profit expressed as a percentage of the wholesale cost: \(\dfrac{9}{45}\times100=20\%\). [2 marks]
Even though the shop marks the price up by \(60\%\) and then reduces it by \(25\%\), the combined multiplier of \(1.2\) shows the sale price still ends up \(20\%\) above the wholesale cost, not at a loss, because the markup was applied to the smaller wholesale figure while the discount was applied to the larger, marked-up retail price.
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