Percentage And Its Applications — Important Questions

10%

Step 1: Given P = ₹10000, A = ₹12100, T = 2 years. We need to find R. Step 2: Use the compound interest formula: A = P(1 + R/100)². Step 3: Substitute values: 12100 = 10000(1 + R/100)². Step 4: Simplify: (1 + R/100)² = 12100/10000 = 1.21 = (1.1)². Step 5: Therefore, 1 + R/100 = 1.1, which gives R = 10%.

4%

Step 1: Initial population = 50000, Final population = 52000. Step 2: Calculate increase: Increase = 52000 - 50000 = 2000. Step 3: Use percent increase formula: Percent increase = (Increase/Original value) × 100. Step 4: Substitute values: Percent increase = (2000/50000) × 100 = 4%. Step 5: Therefore, the population increased by 4%.

₹20000

Step 1: Let income = x. Given: 20% of income = ₹4000. Step 2: Write the equation: (20/100) × x = 4000. Step 3: Simplify: 0.20x = 4000. Step 4: Solve for x: x = 4000/0.20 = 20000. Step 5: Therefore, his income is ₹20000. Verification: 20% of 20000 = 4000 ✓

₹81000

Step 1: Initial value = ₹100000, depreciation rate = 10% per annum, time = 2 years. Step 2: Use depreciation formula: Final value = Initial value × (1 - rate/100)ⁿ. Step 3: Substitute values: Final value = 100000 × (1 - 10/100)². Step 4: Calculate: Final value = 100000 × (0.9)² = 100000 × 0.81 = ₹81000. Step 5: Therefore, the value after 2 years is ₹81000.