Question 13 - Figure it out - Page 28, 29, 30 - Chapter 1 Class 8 - Fractions in Disguise (Ganita Prakash II)

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Question 13 Three shops sell the same items at the same price. The shops offer deals as follows: Shop A: “Buy 1 and get 1 free” Shop B: “Buy 2 and get 1 free” Shop C: “Buy 3 and get 1 free” Answer the following: (i) If the price of one item is ₹100, what is the effective price per item in each shop? Arrange the shops from cheapest to costliest.Here, Price per item = (𝑨𝒎𝒐𝒖𝒏𝒕 𝒑𝒂𝒊𝒅 𝒇𝒐𝒓 𝒕𝒉𝒐𝒔𝒆 𝒊𝒕𝒆𝒎𝒔)/(𝑻𝒐𝒕𝒂𝒍 𝒊𝒕𝒆𝒎𝒔) Shop A (Buy 1 Get 1 Free) Get 2 items for ₹100 Thus, Price per item = 100/2 = ₹ 50 Shop B (Buy 2 Get 1 Free) Get 3 items for ₹200 Thus, Price per item = 200/3 = ₹ 66.66… Shop C (Buy 3 Get 1 Free) Get 4 items for ₹300 Thus, Price per item = 300/4 = ₹ 75 Thus, Order of shops from Cheapest to Costliest: Shop A, Shop B, Shop C Question 13 Three shops sell the same items at the same price. The shops offer deals as follows: Shop A: “Buy 1 and get 1 free” Shop B: “Buy 2 and get 1 free” Shop C: “Buy 3 and get 1 free” Answer the following: (ii) For each shop, calculate the percentage discount on the items. [Hint: Compare the free items to the total items you receive.]Here, Percentage Discount = (𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝑭𝒓𝒆𝒆 𝒊𝒕𝒆𝒎𝒔)/(𝑻𝒐𝒕𝒂𝒍 𝒊𝒕𝒆𝒎𝒔) × 100 Shop A (Buy 1 Get 1 Free) 1 free out of 2 total Thus, Percentage Discount = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐹𝑟𝑒𝑒 𝑖𝑡𝑒𝑚𝑠)/(𝑇𝑜𝑡𝑎𝑙 𝑖𝑡𝑒𝑚𝑠) × 100 = 1/2 × 100 = 50% Shop B (Buy 2 Get 1 Free) 1 free out of 3 total Thus, Percentage Discount = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐹𝑟𝑒𝑒 𝑖𝑡𝑒𝑚𝑠)/(𝑇𝑜𝑡𝑎𝑙 𝑖𝑡𝑒𝑚𝑠) × 100 = 1/3 × 100 = 33.33..% Shop C (Buy 3 Get 1 Free) 1 free out of 4 total Thus, Percentage Discount = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐹𝑟𝑒𝑒 𝑖𝑡𝑒𝑚𝑠)/(𝑇𝑜𝑡𝑎𝑙 𝑖𝑡𝑒𝑚𝑠) × 100 = 1/4 × 100 = 25 % Question 13 Three shops sell the same items at the same price. The shops offer deals as follows: Shop A: “Buy 1 and get 1 free” Shop B: “Buy 2 and get 1 free” Shop C: “Buy 3 and get 1 free” Answer the following: (iii) Suppose you need 4 items. Which shop would you choose? Why?Let’s look at each shop one-by-one Shop A Use the deal twice (Buy 1, Get 1 Free – 2 times). Pay for 2 Total Cost = 2 × 100 = ₹200 Shop B Buy 2, Get 1 Free (3 items for ₹200) + Buy 1 regular (₹100) Total Cost = 200 + 100 = ₹300 Shop C Buy 3, Get 1 Free Pay for 3 Total Cost = 3 × 100 = ₹300 Final Choice Choose Shop A because it is the cheapest (₹200).