Higher June 2018 Paper 1 Q23
23 A shopkeeper compares the income from sales of a laptop in March and April.
April
| Price | \(\dfrac{1}{5}\) more than March |
| Number sold | \(\dfrac{1}{4}\) less than March |
By what fraction does the income from these sales decrease in April? [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(\dfrac{6}{5}\) or \(\dfrac{3}{4}\) | M1 | oe fractions, decimals or percentages, but not \(\dfrac{6}{5}\) as a mixed number |
| \(\dfrac{6}{5} \times \dfrac{3}{4}\) or \(\dfrac{18}{20}\) or \(\dfrac{9}{10}\) or 0.9 or 90% or 0.1 or 10% | M1dep | oe fractions or decimals, but not \(\dfrac{6}{5}\) as a mixed number |
| \(\dfrac{1}{10}\) | A1 | oe fraction |
| Alternative method 2 | ||
| Chooses value for price and increases by \(\dfrac{1}{5}\) or chooses number of laptops and decreases by \(\dfrac{1}{4}\) | M1 | correct method or value for either eg (£)5 and (£)6 or 20 (laptops) and 15 (laptops) |
| Chooses value for price and increases by \(\dfrac{1}{5}\) and chooses number of laptops and decreases by \(\dfrac{1}{4}\) and \(\dfrac{\text{reduced income}}{\text{original income}}\) (\(\times\) 100) or \(\dfrac{\text{reduction}}{\text{original}}\) (\(\times\) 100) | M1dep | correct method or values eg \(\dfrac{6 \times 15}{5 \times 20}\) (\(\times\) 100) or \(\dfrac{5 \times 20 - 6 \times 15}{5 \times 20}\) (\(\times\) 100) |
| \(\dfrac{1}{10}\) | A1 | oe fraction |
Additional guidance
| For full marks, accept a fraction equivalent to \(\dfrac{1}{10}\) incorrectly simplified, but not converted to a decimal or percentage | M1M1A1 M1M1A0 |
| If both methods tried and answer incorrect, award better method mark | |
| Accept variables in any working for M1M1 |