A corner shop buys tins of soup from a supplier. The supplier raises the wholesale price by 8%, so the shop now pays 54p for each tin. Work out the wholesal...
Question 1 Report
A corner shop buys tins of soup from a supplier. The supplier raises the wholesale price by 8%, so the shop now pays 54p for each tin.
- Work out the wholesale price per tin before the increase. (3)
- The shop sells each tin for 75p. Work out the shop's percentage profit based on the new wholesale price, correct to 1 decimal place. (2)
Answer Details
When the increased price is known, the original price is found by dividing by the increase multiplier, since multiplying the unknown original by that same multiplier is what produced the increased price.
(a) Let the original wholesale price be \(p\). Since an 8% increase means \(p \times 1.08 = 54\):
\[p = 54 \div 1.08\] [1 mark]
\[= 50\text{p}\] [1 mark]
Checking: \(50 \times 1.08 = 54\)p, which matches the new price [1 mark].
(b) Profit is the selling price minus the (new) wholesale cost:
\[75 - 54 = 21\text{p}\] [1 mark]
The percentage profit is this profit as a fraction of the wholesale price actually paid, times 100:
\[\frac{21}{54} \times 100 = 38.888\ldots\% = 38.9\%\] (1 d.p.) [1 mark]
Percentage profit is always measured against the cost price (54p), not the selling price (75p), because profit is defined relative to what was spent.
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