Women Sub Inspector of Police — Trainee — Police — 2016 — Official Paper — Kerala PSC PYQ Practice with Answers

Correct answer (Option C):\nFormula: Product of two numbers = HCF × LCM\nGiven values:\nFirst number = 108\nHCF = 12\nLCM = 216\n\nStep-by-step calculation:\n108 × Second number = 12 × 216\nSecond number = (12 × 216) / 108\nSecond number = 2592 / 108 = 24\nTherefore, the other number is 24.\nOption C is correct.\n\nWhy others are wrong:\nOptions A, B, and D do not satisfy the mathematical property that the product of the two numbers equals the product of their HCF and LCM.\n\nStudy tip:\nAlways remember the relationship between HCF and LCM for two numbers: Product = HCF × LCM. This formula is highly recurring in competitive exams.

Correct answer (Option A):\nA prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Among the given options, 2 has only two divisors: 1 and 2. Therefore, 2 is a prime number. In fact, it is the only even prime number.\nOption A is correct.\n\nWhy others are wrong:\nOption B (6) is a composite number divisible by 1, 2, 3, and 6. Option C (9) is a composite number divisible by 1, 3, and 9. Option D (1) is neither prime nor composite by definition.\n\nStudy tip:\nRemember that 2 is the smallest prime number and the only even prime number. All other prime numbers are odd.

Correct answer (Option D):\nFormula:\nCost Price (CP) = [Selling Price (SP) × 100] / (100 + Profit%)\n\nGiven values:\nSP = ₹448\nProfit% = 12%\n\nStep-by-step working:\nCP = (448 × 100) / (100 + 12)\nCP = 44800 / 112\nCP = 400\nThus, the cost price of the article is Rs. 400.\nOption D is correct.\n\nWhy others are wrong:\nOptions A, B, and C represent incorrect calculations and do not lead to a 12% profit when sold at ₹448.\n\nStudy tip:\nWhen profit is made, Selling Price is always greater than Cost Price. Expressing it as SP = CP × 1.12 is a faster way to solve such problems.

Correct answer (Option C):\nWhen four numbers a, b, c, d are in proportion, the ratio of the first two equals the ratio of the last two:\na / b = c / d\n\nGiven numbers: 3, 5, p+5, 25\n3 / 5 = (p + 5) / 25\n\nCross-multiplying:\n3 × 25 = 5 × (p + 5)\n75 = 5p + 25\n5p = 75 - 25\n5p = 50\np = 10\nOption C is correct.\n\nWhy others are wrong:\nPlugging in options A (15), B (20), or D (30) into the term (p+5) results in ratios that do not equal 3/5.\n\nStudy tip:\nAlternatively, use the rule: Product of extremes = Product of means. Thus, 3 × 25 = 5 × (p + 5), which simplifies the math quickly.

Correct answer (Option A):\nFormula for combined work time:\nTime taken together = (x × y) / (x + y)\n\nGiven values:\nTime taken by A (x) = 10 days\nTime taken by B (y) = 15 days\n\nStep-by-step working:\nTime = (10 × 15) / (10 + 15)\nTime = 150 / 25\nTime = 6 days\nTherefore, they will complete the work together in 6 days.\nOption A is correct.\n\nWhy others are wrong:\nOptions B, C, and D are numerically incorrect values resulting from faulty calculations or misapplying formulas.\n\nStudy tip:\nAlternatively, you can use the LCM method. LCM of 10 and 15 is 30 (Total Work). Efficiency of A = 3, Efficiency of B = 2. Total efficiency = 5. Days = 30 / 5 = 6 days.