Example 13 - Chapter 1 Class 8 - Fractions in Disguise (Ganita Prakash II)

Transcript

Example 13 After Surbhi bought cookware from the wholesaler, she kept a profit margin of 50% on all the products. To clear off the remaining stock, she thought she would offer a 50% discount and come out without any loss. (i) Do you think she didn’t make any loss? (ii) If she had sold goods (originally) for ₹12,000 after discount, how much loss did she incur? What is the percentage loss? (iii) What should have been the percentage discount offered so that she sold the goods at the price she had bought (i.e., no profit or loss)?Let's use algebra to see why Surbhi made a mistake. Let the original price she bought the goods for (Cost Price) be 𝒙. She marks it up 50%: New Price =𝑥+0.5𝑥=𝟏.𝟓𝒙 She discounts it 50% from the new price: Discount =50% of 1.5𝑥=𝟎.𝟕𝟓𝒙 Final Selling Price =1.5𝑥−0.75𝑥=𝟎.𝟕𝟓𝒙 Now, let's answer the questions: Do you think she didn't make any loss? She definitely made a loss! She bought the items for 𝑥 (which is 𝟏𝒙 ), but sold them for 𝟎.𝟕𝟓𝒙. She lost 𝟐𝟓% of her money. (ii) If she sold goods originally worth ₹12,000 after the discount, what is her loss? The selling price ( 0.75𝑥 ) is equal to ₹12,000. 0.75𝑥=12000 75/100 × 𝑥=12000 𝑥=12000 ×100/75 𝒙=𝟏𝟔,𝟎𝟎 Her original cost was ₹16,000. She sold it for ₹12,000. Her loss is ₹4,000 (which is a 𝟐𝟓% loss). (iii) What discount should she have offered to break even? She needs the final price to go from 1.5𝑥 back down to exactly 𝑥. She needs to remove 𝟎.𝟓𝒙. What percentage of 𝟏.𝟓𝒙 is 𝟎.𝟓𝒙 ? 0.5𝑥/1.5𝑥=1/3≈𝟑𝟑.𝟑𝟑% Thus, she should have offered a 33.33% discount