Percentages (Copy)

IGCSE Mathematics 0580 – Percentage Calculations Practice Exam
Divided into Paper 1 (No Calculator) and Paper 2 (Calculator Allowed)
With Full Worked Solutions

Paper 1: Non-Calculator Section

Q1. Find 25% of 320.
Solution:
25% = ¼
¼ × 320 = 80
Answer: 80

Q2. Express 18 as a percentage of 60.
Solution:
(18 ÷ 60) × 100
= (3 ÷ 10) × 100 = 30%
Answer: 30%

Q3. A bag was sold at a 10% discount. If the original price was ₨240, what was the sale price?
Solution:
10% of 240 = (1/10) × 240 = 24
Sale price = 240 – 24 = ₨216
Answer: ₨216

Q4. A toy was bought for ₨150 and sold for ₨180.
Find the percentage profit.
Solution:
Profit = 180 – 150 = ₨30
% Profit = (30 ÷ 150) × 100 = 20%
Answer: 20%

Q5. After a 20% increase, the price of a book became ₨180. What was the original price?
Solution:
Let original price = x
x + 20% of x = 180
x + 0.2x = 180
1.2x = 180
x = 180 ÷ 1.2 = 150
Answer: ₨150

Paper 2: Calculator Allowed Section

Q6. A jacket is priced at ₨3,500. A 12% discount is offered.
a) Calculate the discount.
b) Find the final price after discount.
Solution:
a) (12 ÷ 100) × 3500 = ₨420
b) 3500 – 420 = ₨3080
Answer: ₨420, ₨3080

Q7. A student scored 42 out of 56 in an exam. What is the percentage score?
Solution:
(42 ÷ 56) × 100 = 75%
Answer: 75%

Q8. A car worth ₨2,200,000 is bought with a 25% deposit. Find:
a) The deposit paid
b) The balance remaining
Solution:
a) (25 ÷ 100) × 2,200,000 = ₨550,000
b) 2,200,000 – 550,000 = ₨1,650,000
Answer: ₨550,000, ₨1,650,000

Q9. A man invests ₨18,000 for 3 years at 5% simple interest per annum. Find the total interest.
Solution:
SI = (P × R × T) ÷ 100
= (18,000 × 5 × 3) ÷ 100
= ₨2,700
Answer: ₨2,700

Q10. Find the compound interest on ₨10,000 for 2 years at 6% per annum.
Solution:
Amount = P(1 + r/100)^n
= 10,000 × (1.06)^2 = 10,000 × 1.1236 = ₨11,236
CI = 11,236 – 10,000 = ₨1,236
Answer: ₨1,236

Q11. The price of a sofa increased from ₨45,000 to ₨49,500. Find the percentage increase.
Solution:
Increase = 49,500 – 45,000 = ₨4,500
% Increase = (4500 ÷ 45,000) × 100 = 10%
Answer: 10%

Q12. A computer depreciates by 15% annually. If current value is ₨85,000, what will it be after 2 years?
Solution:
Value after 2 years = 85,000 × (1 – 0.15)^2
= 85,000 × 0.85^2 = 85,000 × 0.7225 = ₨61,412.5
Answer: ₨61,413 (rounded to nearest rupee)

Q13. A shopkeeper earns 6.5% commission on sales of ₨75,000.
Calculate her commission.
Solution:
(6.5 ÷ 100) × 75,000 = ₨4,875
Answer: ₨4,875

Q14. A man paid ₨1,104 including 15% tax. What was the price before tax?
Solution:
Let original price = x
x + 15% of x = 1104
1.15x = 1104
x = 1104 ÷ 1.15 = ₨960
Answer: ₨960

Q15. A fridge was increased by 8% in January and decreased by 5% in March. Original price = ₨50,000
Find the price after both changes.
Solution:
After 8% increase:
= 50,000 × 1.08 = ₨54,000
After 5% decrease:
= 54,000 × 0.95 = ₨51,300
Answer: ₨51,300

Q16. A woman received ₨2,400 interest after investing at 4% simple interest for 3 years.
Find the principal.
Solution:
SI = (P × R × T) ÷ 100
2400 = (P × 4 × 3) ÷ 100
2400 = (12P) ÷ 100 → P = (2400 × 100) ÷ 12 = ₨20,000
Answer: ₨20,000