Question
A seller marked the price of an item at Rs. 5,000. The
seller gave successive discounts of (b + 5)% and (b - 5)% to a customer. If the customer paid Rs. 4,050 for the item, then find the value of 'b'.Solution
ATQ; SP of the item = 5000 × (1 - (b + 5)/100) × (1 - (b - 5)/100) = 4050 or, {(100 - b - 5)/100} × {(100 - b + 5)/100} = 4050/5000 or, (95 - b) × (105 - b) = (4050/5000) × 100 × 100 or, 95 × 105 - 95b - 105b + b² = 8100 or, b² - 200b + 9975 - 8100 = 0 or, b² - 200b + 1875 = 0 or, b² - 10b - 190b + 1875 = 0 or, b × (b - 10) - 187 × (b - 10) = 25 or, (b - 10) × (b - 187) = 25 So, b = 10 or b = 187 But, b = 187 is not possible because the discount cannot be more than 100%. Therefore, b = 10
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