Calculate 15% of 200
Worked Solution & Answer
Find 10% (divide by 10) and 1% (divide by 100), or multiply by the decimal multiplier.
e.g. 15% of 60 = 6 + 3 = 9
30
e.g. 15% of 60 = 6 + 3 = 9
30
Answer: 30
Percentage change — Notes & Worked Examples Show / Hide
Explanation:
To calculate the percentage change (or percentage profit / loss), first subtract the two amounts to find the actual change, then divide by the original amount and multiply by 100: Percentage Change = ChangeOriginal × 100.
A very common exam mistake is dividing by the new amount instead of the original amount. Always check which value came first in time and put that original value on the bottom of the fraction.
Example 1: A jacket is reduced in a sale from £80 to £68. Work out the percentage decrease.
Solution:
Change = £80 − £68 = £12
Original price = £80
% decrease = 1280 × 100 = 0.15 × 100
Answer: 15%
Example 2: A house was bought for £160,000 and sold for £196,000. Calculate the percentage profit.
Solution:
Profit (change) = 196,000 − 160,000 = £36,000
% profit = 36,000160,000 × 100
= 0.225 × 100 = 22.5%
Answer: 22.5%
Calculate 7.5% of £320
£
Worked Solution & Answer
Find 10% (divide by 10) and 1% (divide by 100), or multiply by the decimal multiplier.
e.g. 15% of 60 = 6 + 3 = 9
£24
e.g. 15% of 60 = 6 + 3 = 9
£24
Answer: £ £24
Charlotte bought an apartment for \$750 000
In the first year, the value of the apartment decreased by 4%
In the second year, the value of the apartment decreased by 6.5%
In the third year, the value of the apartment increased by x%
At the end of the third year, the value of Charlotte's apartment was \$698 445
Work out the value of x
In the first year, the value of the apartment decreased by 4%
In the second year, the value of the apartment decreased by 6.5%
In the third year, the value of the apartment increased by x%
At the end of the third year, the value of Charlotte's apartment was \$698 445
Work out the value of x
x =
Worked Solution & Answer
End of year 2 = 750 000 × 0.96 × 0.935 = $673 200 M2
Multiplier in year 3 = 698 445 ÷ 673 200 = 1.0375 ⇒ x = 3.75 A1
Multiplier in year 3 = 698 445 ÷ 673 200 = 1.0375 ⇒ x = 3.75 A1
Answer: x = 3.75
A rectangle has length 60 cm and width 40 cm
The length decreases by 15%
The width decreases by 10%
The length decreases by 15%
The width decreases by 10%
Is she correct?
You must show calculations to support your answer.
You must show calculations to support your answer.
Sue says,
‘‘The perimeter decreases by 25% because 15% + 10% is 25%’’
‘‘The perimeter decreases by 25% because 15% + 10% is 25%’’
Conclusion:
Worked Solution & Answer
Original perimeter = 2(60 + 40) = 200 cm M1
New length = 60 × 0.85 = 51 cm
New width = 40 × 0.90 = 36 cm M1
New perimeter = 2(51 + 36) = 174 cm
Decrease in perimeter = 200 - 174 = 26 cm M1
Percentage decrease = 26200 × 100% = 13%
She is incorrect because percentages cannot simply be added
the actual decrease is 13%. A1
New length = 60 × 0.85 = 51 cm
New width = 40 × 0.90 = 36 cm M1
New perimeter = 2(51 + 36) = 174 cm
Decrease in perimeter = 200 - 174 = 26 cm M1
Percentage decrease = 26200 × 100% = 13%
She is incorrect because percentages cannot simply be added
the actual decrease is 13%. A1
Answer: Conclusion: No (perimeter decreases by 13%)
Single bag of crisps is 55p. A multipack of 6 bags costs 10% less than 6 single bags. Work out the cost of the multipack. [4 marks]
The multipack costs 10% **less** than 6 single bags.
Work out the cost of the multipack.
Work out the cost of the multipack.
Answer £
Worked Solution & Answer
6 single bags = 6 × 55p = 330p. M2
10% of 330p = 33p M1
Multipack cost = 330 - 33 = 297p = £2.97. A1
10% of 330p = 33p M1
Multipack cost = 330 - 33 = 297p = £2.97. A1
Answer: Answer £ 2.97
28 is increased by 25%
40 is decreased by 15%
40 is decreased by 15%
Which answer is bigger?
Show how you decide.
Show how you decide.
Answer
Worked Solution & Answer
28 increased by 25%: M1
25% of 28 = 7.
28 + 7 = 35. M1
40 decreased by 15%:
15% of 40 = 6. M1
40 - 6 = 34
Since 35 > 34, 28 increased by 25% is bigger. A1
25% of 28 = 7.
28 + 7 = 35. M1
40 decreased by 15%:
15% of 40 = 6. M1
40 - 6 = 34
Since 35 > 34, 28 increased by 25% is bigger. A1
Answer: Answer 28 increased by 25% (35 is bigger than 34)
Carly’s total annual pay = salary + bonus
@@TABULAR0@@
Work out the percentage change in her total annual pay.
State whether it is an increase or a decrease.
@@TABULAR0@@
Work out the percentage change in her total annual pay.
State whether it is an increase or a decrease.
Answer
Worked Solution & Answer
Last year total = £26 000 + £4000 = £30 000 M1
This year salary = £26 000 × 1.06 = £27 560 M1
This year bonus = £4000 × 0.91 = £3640 M1
This year total = £27 560 + £3640 = £31 200
Change = +£1200 ⇒ (1200 / 30 000) × 100 = 4% increase. A1
This year salary = £26 000 × 1.06 = £27 560 M1
This year bonus = £4000 × 0.91 = £3640 M1
This year total = £27 560 + £3640 = £31 200
Change = +£1200 ⇒ (1200 / 30 000) × 100 = 4% increase. A1
Answer: Answer 4% increase
Alec bought a house.
By the end of the first year, the value of Alec’s house had increased by 1%.
By the end of the second year, its value had decreased by 10% of its value at the end of the first year.
Use multipliers to work out the overall percentage decrease in the value of Alec’s house for this two-year period.
By the end of the first year, the value of Alec’s house had increased by 1%.
By the end of the second year, its value had decreased by 10% of its value at the end of the first year.
Use multipliers to work out the overall percentage decrease in the value of Alec’s house for this two-year period.
%
Worked Solution & Answer
Multiplier for 1% increase = 1 + 0.01 = 1.01 M1
Multiplier for 10% decrease = 1 - 0.10 = 0.90 M1
Overall multiplier = 1.01 × 0.90 = 0.909 M1
Percentage decrease = (1 - 0.909) × 100% = 0.091 × 100% = 9.1%. A1
Multiplier for 10% decrease = 1 - 0.10 = 0.90 M1
Overall multiplier = 1.01 × 0.90 = 0.909 M1
Percentage decrease = (1 - 0.909) × 100% = 0.091 × 100% = 9.1%. A1
Answer: 9.1% %
(b) Amaya creates this line graph to show the same data. [4 marks]
Work out the percentage increase in the number of computer tablet users from 2014 to 2018.
%
Worked Solution & Answer
(b)
2014 value = 0.8 billion M2
2018 value = 1.4 billion M1
Percentage increase = [(1.4 − 0.8) ÷ 0.8] × 100 = (0.6 ÷ 0.8) × 100 = 75%. A1
2018 value = 1.4 billion M1
Percentage increase = [(1.4 − 0.8) ÷ 0.8] × 100 = (0.6 ÷ 0.8) × 100 = 75%. A1
Answer (b): 75 %
Q is directly proportional to √(t)
The graph shows the relationship between Q and t for 0 < t < 8
The graph shows the relationship between Q and t for 0 < t < 8
(a) Find a formula for Q in terms of t [3 marks]
Q =
(b) Find the percentage increase in t [2 marks]
%
Worked Solution & Answer
(a)
Q = k√t M2
Using (4, 6): 6 = k√4 => k = 3 => Q = 3√t A1
Using (4, 6): 6 = k√4 => k = 3 => Q = 3√t A1
Answer (a): Q = Q = 3√(t)
(b)
Since t ∝ Q², multiplier for t is 1.2² = 1.44 => 44% increase M1 A1
Answer (b): 44 %