The ratio between the marked price and cost price of an article is B:A respectively. The ratio between the selling price and marked price of the article is (B+2):(B+3) respectively. If the discount given on the article while selling is Rs. 50 and the marked price of the article is Rs. 300, then which of the following statements is/are correct? (It is assumed that the article is marked 50% above its cost price.)

(i) The profit on the article while selling is Rs. 100. 

(ii) The value of ‘B’ is a prime number.

(iii) The cost price of the article is multiple of 12.

Solution

If the discount given on the article while selling is Rs. 50 and the marked price of the article is Rs. 300. Marked price of the article = Rs. 300 Discount = Rs. 50 Selling price of the article = 300-50 = Rs. 250 The ratio between the selling price and marked price of the article is (B+2):(B+3) respectively. (B+2)/(B+3) = 250/300 (B+2)/(B+3) = 5/6 6B+12 = 5B+15 6B-5B = 15-12 B = 3 ratio between the selling price and marked price of the article = (B+2):(B+3) = (3+2):(3+3) = 5:6    Eq.(i) The ratio between the marked price and cost price of an article is B:A respectively. marked price : cost price = B:A = 3 : A   Eq.(ii) From Eq.(i) and Eq.(ii), marked price : selling price : cost price = 3x2 : 5 : 2A  = 6 : 5 : 2A It is assumed that the article is marked 50% above its cost price. Let’s assume the cost price of the article is 6y. Then cost price = 2Ay 6y = (100+50)% of 2Ay 6 = (150 x 2A)/100 6 = (300A)/100 A = 2 So marked price : selling price : cost price = 6 : 5 : 2A = 6 : 5 : 2x2 = 6 : 5 : 4 We know that the marked price of the article is Rs. 300 and the selling price of the article is Rs. 250. So by the above given ratio, cost price of the article = (300/6)x4 = Rs. 200 (i) The profit on the article while selling is Rs. 100.  profit on the article while selling = selling price - cost price = 250-200 = Rs. 50 So the given statement is not true. (ii) The value of ‘B’ is a prime number. The given statement is true. Because the value of ‘B’ is prime. (iii) The cost price of the article is multiple of 12. cost price of the article = Rs. 200 So the given statement is not true. Because it is not the multiple of 12.