A shopkeeper offers the following discount schemes for the purchase of his goods. Find the scheme which has the maximum discount. (i) Two successive discounts of 20% and 10% (ii) Discount of 10% (iii) Buy 8 and get 4 free (iv) Buy 9 and get 6 free

Explanation

GIVEN: 4 schemes offered by shopkeeper FORMULA USED: S.P. = ( 1- d1/100) × ( 1- d2/100) × M.P. Where, S.P. = Selling price, M.P. = Marked price, and d1 and d2 = successive discounts respectively. Discount =( M.P. - S.P.) Discount% = ( Discount /M.P. )× 100 CALCULATION: Let us assume the Marked price is Rs100. On considering condition (a), we have Here d1 = 20% , d2 = 10% S.P. = ( 1- 20/100) × ( 1- 10/100) × 100 = 80/100 × 90/100 × 100 = Rs 72. Discount = ( 100 - 72) = Rs 28 Discount% =( 28/100) × 100 = 28% On considering condition (c), we have Buy 8 and get 4 free Now, as we have assumed Marked price of 1 article = Rs100 Hence, M.P. of 12 articles = Rs 1200. As the 4 articles are free, Hence, S.P. of 8 articles = Rs 800 ⇔ Discount = (1200 - 800) = Rs400. Discount% = (400/1200) × 100 = 33.33%. On considering condition (d), we have Buy 9 get 6 free, Now, M.P. of 15 articles = Rs1500. As 6 articles are free, Hence, S.P. of 9 articles = Rs900. ⇔ Now, Discount = ( 1500 - 900) = Rs600. Discount% = (600/1500) × 100 = 40% Since condition (d) i.e. Buy 9 get 6 free has maximum discount % i.e. 40%. The answer is (iv)