Govt. Exams
Entrance Exams
SI = 50000×12×2/100 = ₹12,000. CI = 50000(1.12)² - 50000 = ₹12,720. Difference = ₹720.
Using HCF × LCM = Product of two numbers:
15 × 450 = 90 × Other number
6750 = 90 × Other number
Other number = 6750 ÷ 90 = 75
Verification: HCF(90, 75) = 15 ✓ and LCM(90, 75) = 450 ✓
Using the formula: HCF × LCM = Product of two numbers
12 × 180 = 60 × Other number
2160 = 60 × Other number
Other number = 2160 ÷ 60 = 36
Verification: HCF(60, 36) = 12 ✓ and LCM(60, 36) = 180 ✓
Using HCF × LCM = Product: 6 × 60 = 12 × other. 360 = 12 × other.
Other = 360 ÷ 12 = 30.
HCF × LCM = Product of numbers = 360. 360 = 20 × other number.
Other number = 360 ÷ 20 = 18.
72 = 2³ × 3², 90 = 2 × 3² × 5.
Common factors: 2 and 3². HCF = 2 × 3² = 2 × 9 = 18.
20 = 2² × 5, 30 = 2 × 3 × 5, 40 = 2³ × 5. LCM = 2³ × 3 × 5 = 8 × 3 × 5 = 120.
45 = 3² × 5, 60 = 2² × 3 × 5, 75 = 3 × 5².
Common factors: 3 and 5. HCF = 3 × 5 = 15.
Using the formula: HCF × LCM = Product of two numbers. 15 × LCM = 2700, so LCM = 2700 ÷ 15 = 180.
Using Euclidean algorithm: 126 = 84 × 1 + 42, then 84 = 42 × 2 + 0.
Therefore, HCF(84, 126) = 42.
