Question
Articles 'A' and 'B' are marked (m + n - 9) % and (4m -
8)% respectively, over their respective cost price. Cost price of 'A' is Rs. (100n(m + 2)), which is Rs. '400n' less than that of article 'B'. 'A' is sold after a discount of (4n - 5m - 26) %, whereas 'B' is sold after a discount of Rs. '770m'. (Note: 'm' is the number of prime numbers between 30 and 80, and 'n' = (m² + 32) ÷ 8) Which of the following statement(s) is/are true? I. Ratio of selling price of article 'B' to that of 'A' is 6:5. II. Profit earned on 'B' is less than the profit earned on 'A'. III. Selling price of 'B' is 20% more than the marked price of 'A'.Solution
Prime numbers between 30 and 80 = 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79 So, 'm' = 12 'n' = (12² + 32) ÷ 8 = (144 + 32) ÷ 8 = 176 ÷ 8 = 22 m + n - 9 = 12 + 22 - 9 = 25 4m - 8 = 48 - 8 = 40 100n(m + 2) = 100 × 22 × 14 = 30,800 400n = 400 × 22 = 8,800 4n - 5m - 26 = 88 - 60 - 26 = 2 770m = 770 × 12 = 9,240 Cost price of article 'A' = Rs. 30,800 Cost price of article 'B' = 30,800 + 8,800 = Rs. 39,600 Marked price of article 'A' = 1.25 × 30,800 = Rs. 38,500 Marked price of article 'B' = 1.40 × 39,600 = Rs. 55,440 Selling price of article 'A' = 0.98 × 38,500 = Rs. 37,730 Selling price of article 'B' = 55,440 – 9,240 = Rs. 46,200 Statement I: Required ratio = 46,200 : 37,730 Check with 6:5 → (46,200 × 5 = 231,000) vs (37,730 × 6 = 226,380) → not equal So, statement I is false. Statement II: Profit on 'A' = 37,730 – 30,800 = Rs. 6,930 Profit on 'B' = 46,200 – 39,600 = Rs. 6,600 Since 6,600 < 6,930 So, statement II is true. Statement III: Required percent = [(46,200 – 38,500) ÷ 38,500] × 100
= 7,700 ÷ 38,500 × 100
= 20% more So, statement III is true. Therefore, both statement II and III are true. Hence, option A.
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