Percentage — P5 Mathematics

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Class

Date

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Instructions: This worksheet has 2 sections. Answer all questions. Section A: Foundation (15 questions). Section B: Word Problems & Challenge (26 questions). Show all working. Use a calculator. Total: 41 questions.

Key Concepts Covered

Fraction, decimal, and percentage conversions
Percentage of a quantity and finding the original quantity
Percentage increase and decrease
GST (Goods and Services Tax) calculations — adding GST and reverse GST
Discounts, profit and loss percentage
Mixed word problems with real-life contexts

Section A

Foundation

~15 min

Give your answers correct to 2 decimal places unless stated otherwise.

Express each of the following as a percentage:

(a) 3/4 = ___%
(b) 2/5 = ___%
(c) 7/20 = ___%
(d) 1/8 = ___%
(e) 5/6 = ___% (correct to 2 d.p.)

Express each of the following as a fraction in its simplest form:

(a) 40% = ___
(b) 75% = ___
(c) 12.5% = ___
(d) 60% = ___
(e) 8% = ___

Express each of the following as a percentage:

(a) 0.75 = ___%
(b) 0.03 = ___%
(c) 1.25 = ___%
(d) 0.08 = ___%
(e) 0.667 = ___% (correct to 2 d.p.)

Find each of the following:

(a) 25% of 80 = ___
(b) 35% of 120 = ___
(c) 60% of 45 = ___
(d) 15% of 200 kg = ___ kg
(e) 8% of $350 = $___

Express the first quantity as a percentage of the second:

(a) 15 cm as a % of 60 cm = ___%
(b) 45 g as a % of 900 g = ___%
(c) $3.50 as a % of $28 = ___%
(d) 18 minutes as a % of 2 hours = ___%
(e) 750 ml as a % of 3 litres = ___%

Find the original quantity:

(a) 40% of ___ = 160
(b) 25% of ___ = $75
(c) 12.5% of ___ = 50 kg
(d) 80% of ___ = 320 m
(e) 5% of ___ = $4.50

Find the percentage increase:

(a) $50 increases to $65 → ___%
(b) 80 kg increases to 100 kg → ___%
(c) 45 students increases to 54 students → ___%
(d) $200 increases to $230 → ___%
(e) 1.5 m increases to 2.1 m → ___%

Find the percentage decrease:

(a) $120 decreases to $96 → ___%
(b) 500 g decreases to 375 g → ___%
(c) 72 students decreases to 60 students → ___%
(d) $400 decreases to $340 → ___%
(e) 3.2 km decreases to 2.4 km → ___%

State whether each is an increase or decrease, and find the percentage change:

(a) $30 → $45: ___% ___
(b) 200 m → 150 m: ___% ___
(c) 60 kg → 78 kg: ___% ___
(d) $90 → $72: ___% ___
(e) 4 hours → 5 hours: ___% ___

Find the final value:

(a) $200 increases by 10% then decreases by 10% → $___
(b) 500 kg increases by 20% then decreases by 25% → ___ kg
(c) $800 decreases by 15% then increases by 15% → $___
(d) 360 students increases by 25% then decreases by 20% → ___ students
(e) A price is increased by 25% and then decreased by 20%. What is the net % change? ___%

A survey of 200 students shows that 65% prefer maths, 20% prefer science, and the rest prefer English. How many students prefer English?

A class has 30 students. The bar chart shows that 40% are boys and 60% are girls. How many more girls than boys are there?

Find each of the following:

(a) 30% of 2.5 hours = ___ minutes
(b) 45% of 4 litres = ___ ml
(c) 12.5% of $80 = $___
(d) 60% of 3.6 km = ___ m
(e) 75% of 480 seconds = ___ minutes

Class A has 28 students and 75% passed the test. Class B has 32 students and 62.5% passed the test.

(a) How many students in each class passed?
(b) Which class had more students pass? By how many?

A box contains 40 marbles. 35% are red, 25% are blue, and the rest are green.

(a) How many red marbles?
(b) How many blue marbles?
(c) What percentage are green?
(d) How many green marbles?

Section B

Word Problems

~25 min

Show all your working. Give answers correct to 2 decimal places unless stated otherwise.

A pair of shoes costs $85. During a sale, the shop offers a 20% discount. How much does the customer pay?

A book costs $24 before GST. If the GST rate is 9%, find:

(a) The amount of GST in dollars.
(b) The total price including GST.

A laptop costs $1,247.40 inclusive of 9% GST. Find the price before GST.

A salesperson earns a commission of 5% on all sales. If she sells goods worth $12,400 in one month, how much is her commission?

A family's dinner bill at a restaurant is $156. They decide to leave a 10% tip for the service. How much do they pay in total?

A town has a population of 45,000. If the population increases by 8% each year, find:

(a) The increase in population after one year.
(b) The total population after one year.

A jacket is marked at $180. The shop offers a first discount of 15%, and then an additional 10% off the reduced price. What is the final selling price?

A trader buys a bicycle for $240 and sells it for $300. Find:

(a) The profit made.
(b) The percentage profit based on the cost price.

A shopkeeper buys a TV for $850 and sells it at a loss of 12%. Find the selling price.

A family buys the following items:

Rice $12.90
Milk $4.50
Bread $3.80
Eggs (dozen) $5.60

If GST of 9% is charged on all items, find the total amount payable.

In a school with 480 students, 65% are girls. Of the girls, 30% wear glasses. How many girls wear glasses?

A farmer has a field of 12 hectares. He plants rice on 40% of the land, vegetables on 25% of the remaining land, and leaves the rest as fallow.

(a) How many hectares are planted with rice?
(b) How many hectares are planted with vegetables?
(c) What percentage of the total land is fallow?
(d) How many hectares are fallow?

A tourist exchanges $500 SGD into Malaysian Ringgit (MYR) at a rate of 1 SGD = 3.20 MYR. He spends 45% of his MYR during the trip.

(a) How many MYR does he receive?
(b) How much MYR does he spend?
(c) What percentage of his original SGD has he spent? (correct to 2 d.p.)

Sarah saves $60 per month. In January, she saves her usual amount plus an extra 15% bonus from her allowance.

(a) How much does she save in January?
(b) What is her total savings for the first two months (January and February)?
(c) If she continues saving $60 per month, how many more months will it take to reach $1,000? (correct to nearest whole number)

Shop A sells a backpack for $65. Shop B sells the same backpack for $72 but offers a 10% discount.

(a) What is the selling price at Shop B after the discount?
(b) Which shop offers the better deal? By how much?
(c) Express the difference as a percentage of Shop A's original price (correct to 2 d.p.).

A family goes to a supermarket and buys the following:

Fresh vegetables $18.50 (GST-free)
Bread $4.20 (GST-free)
Juice $6.80
Cheese $9.40

If GST of 9% is charged only on non-GST-free items, find the total amount payable.

The price of a concert ticket increases by 20% in the first year and then decreases by 15% in the second year. If the original price was $80, find:

(a) The price after the first year.
(b) The price after the second year.
(c) The overall percentage change from the original price (correct to 2 d.p.).

The ratio of boys to girls in a school is 3 : 5. What percentage of the students are boys?

A car's fuel tank holds 50 litres. After a trip, only 12 litres remain.

(a) What percentage of the fuel was used?
(b) If the car travels 14 km per litre, how far did it travel on this trip?

A survey of 240 parents shows the following preferences for their children's after-school activities:

Sports: 35%
Musical instruments: 25%
Art and craft: 20%
Coding: the rest

(a) How many parents prefer coding?
(b) What percentage prefer coding?
(c) How many more parents prefer sports than musical instruments?
(d) Express the number of art and craft students as a percentage of those who prefer coding (correct to 2 d.p.).

A smartphone is priced at $899 before GST. During a promotion, the shop offers a 15% discount on the price, and then charges 9% GST on the discounted price.

(a) What is the discounted price?
(b) How much GST is charged? (correct to 2 d.p.)
(c) What is the final price inclusive of GST? (correct to 2 d.p.)
(d) What is the overall percentage discount from the original price, including GST? (correct to 2 d.p.)

A family's monthly expenses are distributed as follows. If their total monthly income is $4,200:

Housing: 35%
Food: 22%
Transportation: 13%
Education: 15%
Savings: 10%
Others: the rest

(a) How much do they spend on housing?
(b) What percentage is spent on "Others"?
(c) How much is spent on "Others"?
(d) If the family wants to increase their savings by 5 percentage points, what would be the new savings amount? (Assuming other expenses remain the same.)

A savings account earns 5% interest per annum, compounded annually. If $2,000 is deposited:

(a) How much interest is earned in the first year?
(b) What is the total amount after one year?
(c) How much interest is earned in the second year? (correct to 2 d.p.)
(d) What is the total amount after two years? (correct to 2 d.p.)
(e) What is the overall percentage increase after two years? (correct to 2 d.p.)

A furniture set is priced at $2,500 before GST. The shop offers a 12% discount, but the customer must still pay 9% GST on the discounted price.

(a) What is the discounted price?
(b) How much GST is charged? (correct to 2 d.p.)
(c) What is the final price inclusive of GST? (correct to 2 d.p.)
(d) If the customer had paid full price without discount, how much more would they have paid including GST? (correct to 2 d.p.)
(e) What is the effective overall percentage saved compared to paying full price with GST? (correct to 2 d.p.)

An electronics store sells a tablet for $650 before GST. During a special sale, a member gets an additional 8% discount, and GST of 9% is charged on the final discounted price. If Anna is a member and buys this tablet:

(a) What is the price after the member discount?
(b) How much GST does she pay? (correct to 2 d.p.)
(c) What is her total payment? (correct to 2 d.p.)
(d) If a non-member buys the same tablet, how much more do they pay in total? (correct to 2 d.p.)

A family budgets their monthly income of $5,600 as follows. Find:

Housing: 30%
Food: 20%
Transportation: 12%
Education (for 2 children): equal amount each
Savings: 15%
Insurance: 8%
Miscellaneous: the rest

(a) Amount spent on housing.
(b) Amount spent on food.
(c) Amount each child spends on education.
(d) Percentage spent on miscellaneous. (correct to 2 d.p.)
(e) If the family increases savings by $200, what is the new percentage saved? (correct to 2 d.p.)

Answer Key

Q1: (a) 75% (b) 40% (c) 35% (d) 12.5% (e) 83.33%

Q2: (a) 2/5 (b) 3/4 (c) 1/8 (d) 3/5 (e) 2/25

Q3: (a) 75% (b) 3% (c) 125% (d) 8% (e) 66.67%

Q4: (a) 20 (b) 42 (c) 27 (d) 30 kg (e) $28

Q5: (a) 25% (b) 5% (c) 12.5% (d) 15% (e) 25%

Q6: (a) 400 (b) $300 (c) 400 kg (d) 400 m (e) $90

Q7: (a) 30% (b) 25% (c) 20% (d) 15% (e) 40%

Q8: (a) 20% (b) 25% (c) 16.67% (d) 15% (e) 25%

Q9: (a) 50% increase (b) 25% decrease (c) 30% increase (d) 20% decrease (e) 25% increase

Q10: (a) $198 (b) 450 kg (c) $773.50 (d) 360 students (e) 0% net change

Q11: 200 × 0.65 = 130 maths, 200 × 0.20 = 40 science, 200 − 170 = 30 prefer English

Q12: Boys: 30 × 0.40 = 12. Girls: 30 × 0.60 = 18. Difference: 6 more girls

Q13: (a) 90 min (b) 1800 ml (c) $10 (d) 2160 m (e) 6 minutes

Q14: (a) A: 28 × 0.75 = 21, B: 32 × 0.625 = 20 (b) Class A by 1

Q15: (a) 14 red (b) 10 blue (c) 40% green (d) 16 green

Q16: $85 × 0.20 = $17 discount. Pay: $85 − $17 = $68

Q17: (a) GST = $24 × 0.09 = $2.16 (b) Total = $24 + $2.16 = $26.16

Q18: Price before GST = $1,247.40 ÷ 1.09 = $1,144.40

Q19: Commission = $12,400 × 0.05 = $620

Q20: Tip = $156 × 0.10 = $15.60. Total = $156 + $15.60 = $171.60

Q21: (a) Increase: 45,000 × 0.08 = 3,600 (b) Total: 48,600

Q22: After 1st discount: $180 × 0.85 = $153. After 2nd: $153 × 0.90 = $137.70

Q23: (a) Profit = $300 − $240 = $60 (b) % profit = 60/240 × 100 = 25%

Q24: Selling price = $850 × 0.88 = $748

Q25: Subtotal = $12.90 + $4.50 + $3.80 + $5.60 = $26.80. GST = $26.80 × 0.09 = $2.412. Total = $29.21

Q26: Girls: 480 × 0.65 = 312. Girls with glasses: 312 × 0.30 = 93 girls

Q27: (a) Rice: 12 × 0.40 = 4.8 ha (b) Remaining: 7.2 ha. Veg: 7.2 × 0.25 = 1.8 ha (c) Fallow: 7.2 − 1.8 = 5.4 ha → 5.4/12 × 100 = 45% (d) 5.4 ha

Q28: (a) $500 × 3.20 = 1,600 MYR (b) Spent: 1,600 × 0.45 = 720 MYR (c) 720/3.20 = $225 spent → 225/500 × 100 = 45%

Q29: (a) Jan: $60 + ($60 × 0.15) = $60 + $9 = $69 (b) Total 2 months: $69 + $60 = $129 (c) Need $871 more → 871/60 = 14.52 → 15 months

Q30: (a) Shop B: $72 × 0.90 = $64.80 (b) Shop B by $0.20 (c) 0.20/65 × 100 = 0.31%

Q31: GST items: $6.80 + $9.40 = $16.20. GST = $16.20 × 0.09 = $1.458. Total = $18.50 + $4.20 + $16.20 + $1.458 = $40.36

Q32: (a) $80 × 1.20 = $96 (b) $96 × 0.85 = $81.60 (c) Net change: (81.60 − 80)/80 × 100 = +2%

Q33: Boys % = 3/(3+5) × 100 = 37.5%

Q34: (a) Used: (50 − 12)/50 × 100 = 76% (b) Distance: 38 × 14 = 532 km

Q35: Coding: 100 − (35+25+20) = 20%. (a) 240 × 0.20 = 48 students (b) 20% (c) 240×0.35 − 240×0.25 = 84−60 = 24 more (d) Art: 48, Coding: 48 → 48/48 × 100 = 100%

Q36: (a) $899 × 0.85 = $764.15 (b) GST: $764.15 × 0.09 = $68.77 (c) Total: $764.15 + $68.77 = $832.92 (d) Full with GST: $899 × 1.09 = $979.91. Saved: ($979.91 − $832.92)/$979.91 × 100 = 15.00%

Q37: (a) Housing: $4,200 × 0.35 = $1,470 (b) Others: 100 − (35+22+15+10+8) = 10% (c) $4,200 × 0.10 = $420 (d) New savings: 20% → $4,200 × 0.20 = $840

Q38: (a) Year 1 interest: $2,000 × 0.05 = $100 (b) Total after 1 yr: $2,100 (c) Year 2 interest: $2,100 × 0.05 = $105.00 (d) Total after 2 yrs: $2,205.00 (e) Overall % increase: ($2,205 − $2,000)/$2,000 × 100 = 10.25%

Q39: (a) Discounted: $2,500 × 0.88 = $2,200 (b) GST: $2,200 × 0.09 = $198.00 (c) Total: $2,398.00 (d) Full with GST: $2,500 × 1.09 = $2,725. Difference: $2,725 − $2,398 = $327.00 (e) Saved: $327/$2,725 × 100 = 12.00%

Q40: (a) Member price: $650 × 0.92 = $598.00 (b) GST: $598 × 0.09 = $53.82 (c) Total: $651.82 (d) Non-member total: $650 × 1.09 = $708.50. Difference: $708.50 − $651.82 = $56.68

Q41: (a) Housing: $5,600 × 0.30 = $1,680 (b) Food: $5,600 × 0.20 = $1,120 (c) Education total: $5,600 × 0.15 = $840 → each child: $420 (d) Misc: 100 − (30+20+12+15+15+8) = 0%, amount = $0 (e) New savings: ($5,600 × 0.15 + $200)/$5,600 × 100 = $1,040/$5,600 × 100 = 18.57%