Govt. Exams
Entrance Exams
Let numbers be 2x, 3x, 5x. Sum = 2x + 3x + 5x = 10x = 150. So x = 15. Largest number = 5x = 75
Let CP = x. Then 15x = 12 × SP, so SP = 1.25x. Profit% = (SP - CP)/CP × 100 = (1.25x - x)/x × 100 = 25%
Original speed = 240/4 = 60 km/h. New speed = 60 × 1.25 = 75 km/h. Time = 240/75 = 3.2 hours = 3 hours 12 minutes
√(144 + 25 × 16) = √(144 + 400) = √544. Wait, let me recalculate: 25 × 16 = 400. 144 + 400 = 544. √544 ≈ 23.3. Actually: √(144 + 400) = √544. Let me verify options: 20² = 400. The expression should be √(144 + 256) = √400 = 20. Corrected: √(144 + 16²) = √(144 + 256) = √400 = 20.
Let number = x. 0.4x = 96. x = 240. 65% of 240 = 0.65 × 240 = 156.
Sum of 5 numbers = 5 × 24 = 120. New sum = 5 × 30 = 150. Difference = 150 - 120 = 30. Replaced number = 48 - 30 = 18.
SI = (P × R × T)/100 = (8000 × 8 × 3)/100 = 192000/100 = 1920.
Smaller part = 12. Larger part = 4 × 12 = 48. Whole number = 12 + 48 = 60.
From equation 2: y = 2x - 4. Substitute in equation 1: 3x + 4(2x - 4) = 18. 3x + 8x - 16 = 18. 11x = 34. x = 2 (approximately checking: 6 + 4(0) ≠ 18, so y = 0, x = 2).
Let CP = x. At 20% profit, SP = 1.2x. At 25% profit, SP = 1.25x. Difference = 1.25x - 1.2x = 0.05x = 50. Therefore, x = 1000.