Number 4
3 marks · HardA large TV loses 15% of its value in the first year after purchase, and then loses another 10% of its remaining value in the second year. The TV originally cost $2,400.
Calculate the value of the TV after the first year.
Calculate the value of the TV after the second year.
Calculate the total percentage loss in value over the two years. Give your answer to 1 decimal place.
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.
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(a) $2,040 USD
(b) $1,836 USD
(c) 23.5%
Common mistakes: Adding losses (15% + 10% = 25%) instead of using compound method; not applying percentage to the reduced value in year 2
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Finds 85% of $2,400 correctly: $2,040.
M2 (b) · 1 mark · Finds 90% of value after 1st year (i.e., $2,040 × 0.90): $1,836. (follow-through)
A1 (c) · 1 mark · Calculates loss: $2,400 to $1,836, finds and states correct total percentage loss (to 1 decimal place): 23.5%. (follow-through)
Worked solution
a) After 1st year: 85% of $2,400 = $2,400 × 0.85 = $2,040
b) After 2nd year: 90% of $2,040 = $2,040 × 0.90 = $1,836
c) Loss = $2,400 − $1,836 = $564
Percentage loss = ($564 ÷ $2,400) × 100 = 23.5% (1 decimal place)