Number 4
4 marks · HardA painting is sold for €25,310 after its price first increases by 6% at the end of 1 year and then further increases by 4% at the end of the next year.
Work out the original price of the painting before any increases.
By how much did the price increase in total over the two years? Give your answer to the nearest euro.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) €22,800 EUR
(b) €2,510 EUR
Common mistakes: Adding 6% and 4% to get 10% total increase, instead of applying compound percentages; dividing by 1.1 instead of correct compound factor
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Uses correct reverse compound percentage method: divides by both 1.04 and 1.06 (or by 1.04×1.06) to find the original price.
A1 (a) · 2 marks · Correctly calculates original price to within 1 euro: €22,800 (accept 1 round-off error if work is otherwise correct). (follow-through)
B1 (b) · 1 mark · Finds correct total increase (selling price minus original), to nearest euro: €2,510. (follow-through)
Worked solution
Let the original price be x.
Total increase: €25,310 - €22,800 = €2,510.