Assistant Jailor Grade I / Armed Police SI Trainee / Excise Inspector — 2014 — Official Paper — Kerala PSC PYQ Practice with Answers

Correct answer (Option B):\nFormula for combined work rate: Together time = (A × B) / (A + B)\nGiven:\nJafer's time (A) = 6 days\nShyam's time (B) = 3 days\nStep 1: Together time = (6 × 3) / (6 + 3)\nStep 2: Together time = 18 / 9 = 2 days\nAnswer: 2 days.\nOption B is correct.\n\nWhy others are wrong:\nOption A states 1 day, which is too short. Option C states 4 days, which is longer than Shyam alone. Option D states 5 days, which is mathematically incorrect.\n\nStudy tip:\nWhen working together, the total time taken will always be less than the time taken by the fastest individual worker alone.

Correct answer (Option C):\nFormula for relative speed when moving in opposite directions: Relative Speed = Speed₁ + Speed₂\nGiven:\nTotal distance to cover = 100 m + 150 m = 250 m\nRelative speed = 120 km/h + 80 km/h = 200 km/h\nStep 1: Convert speed to m/s: 200 × (5/18) = 1000 / 18 = 55.56 m/s\nStep 2: Time = Distance / Speed = 250 / (1000 / 18) = (250 × 18) / 1000\nStep 3: Time = 4500 / 1000 = 4.5 seconds\nAnswer: 4.5 sec.\nOption C is correct.\n\nWhy others are wrong:\nOptions A, B, and D do not accurately solve the relative speed and distance requirements, yielding incorrect calculation totals.\n\nStudy tip:\nAlways remember to convert speeds from km/h to m/s by multiplying with 5/18 when distances are given in meters.

Correct answer (Option D):\nFormula: Volume of Cone = Volume of Sphere when melted.\nGiven: Volume of sphere = 4/3 × π × r³ = 36π\nStep 1: 4/3 × r³ = 36 ⇒ r³ = 36 × 3 / 4 = 27\nStep 2: r = 3 cm\nStep 3: Surface area of sphere = 4 × π × r² = 4 × π × 3² = 4 × π × 9 = 36π\nAnswer: 36 π.\nOption D is correct.\n\nWhy others are wrong:\nOptions A, B, and C provide values that do not align with the radius derived from matching standard volume equations.\n\nStudy tip:\nWhen an object is melted and recast into a new shape, its volume remains perfectly constant. Use this to determine missing dimensional variables.

Correct answer (Option B):\nLet present age of Ramu be x and Father be 4x.\nGiven statement: 4 years ago, (x - 4) = √(4x - 4)\nStep 1: Square both sides: (x - 4)² = 4x - 4\nStep 2: x² - 8x + 16 = 4x - 4 ⇒ x² - 12x + 20 = 0\nStep 3: Solve the quadratic equation: (x - 10)(x - 2) = 0\nStep 4: x = 10 (since x = 2 would make age 4 years ago negative).\nAnswer: 10 years.\nOption B is correct.\n\nWhy others are wrong:\nOption A (8) fails the ratio test. Option C (12) fails the square root condition. Option D (40) is the father's age, not Ramu's.\n\nStudy tip:\nTesting the given multiple-choice options directly in the problem conditions is often faster than setting up and resolving complex quadratic functions.

Correct answer (Option A):\nConcept: The smallest number divisible by a set of numbers is their Least Common Multiple (LCM).\nStep 1: Prime factorization:\n8 = 2³\n9 = 3²\n12 = 2² × 3\nStep 2: LCM = Highest power of prime factors = 2³ × 3² = 8 × 9 = 72.\nAnswer: 72.\nOption A is correct.\n\nWhy others are wrong:\nOption B (48) is not divisible by 9. Option C (36) is not divisible by 8. Option D (24) is not divisible by 9.\n\nStudy tip:\nWhen asked for the smallest common divisible number, always look for the LCM. If asked for the highest common dividing factor, locate the HCF.