Govt Exams
Prime factorization: 12=2²×3, 18=2×3², 24=2³×3. LCM = 2³×3² = 8×9 = 72
Average speed = Total distance / Total time = 240/4 = 60 km/h
SI from A = (5000 × 12 × 2)/100 = 1200. SI from B = (3000 × 15 × 2)/100 = 900. Total = 2100. Wait, let me recalculate: SI_A = 1200, SI_B = 900, Total = 2100. Answer should be B. Correcting: SI_A = 1200, SI_B = 900, Total = 2100
Let numbers be x, x+2, x+4. x + x+2 + x+4 = 84 → 3x + 6 = 84 → x = 26. Largest = 30
Let total be 10x. Milk = 7x, Water = 3x. After removal: Milk = 7x - 7, Water = 3x - 3. After adding milk: Milk = 7x - 7 + 10, Water = 3x - 3. Ratio: (7x+3)/(3x-3) = 9/2 → 2(7x+3) = 9(3x-3) → 14x + 6 = 27x - 27 → 13x = 33 → x = 7/√(33/13). Alternative: x = 7, milk = 49
A's rate = 1/15, B's rate = 1/10. Combined rate = 1/15 + 1/10 = 5/30 = 1/6. Time = 6 days
A = P(1 + R/100)^T = 1000(1.1)² = 1000 × 1.21 = 1210
Area = Length × Breadth → 96 = 12 × B → B = 8 cm
23 ÷ 5 = 4 remainder 3. (or 23 = 5×4 + 3)
Total spent = 30% + 40% = 70%. Remaining = 100% - 70% = 30%