Question
A seller marked the price of an item at Rs. 3,000. The
seller gave successive discounts of (y + 3)% and (y - 3)% to a customer. If the customer paid Rs. 2,430 for the item, then find the value of 'y'.Solution
ATQ; SP of the item = 3000 × (1 - (y + 3)/100) × (1 - (y - 3)/100) = 2430 or, {(100 - y - 3)/100} × {(100 - y + 3)/100} = 2430/3000 or, (97 - y) × (103 - y) = (2430/3000) × 100 × 100 or, 97 × 103 - 97y - 103y + y² = 8100 or, y² - 200y + 9991 - 8100 = 0 or, y² - 200y + 1891 = 0 or, y² - 10y - 190y + 1891 = 0 or, y × (y - 10) - 189 × (y - 10) = 10 or, (y - 10) × (y - 189) = 10 So, y = 10 or y = 189 But, y = 189 is not possible because the discount cannot be more than 100%. Therefore, y = 10
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