A seller marked the price of an item at Rs. 2,800. The seller gave successive discounts of (a + 3)% and (a - 3)% to a customer. If the customer paid Rs. 2,268 for the item, then find the value of 'a'.

Solution

ATQ; SP of the item = 2800 × (1 - (a + 3)/100) × (1 - (a - 3)/100) = 2268 or, {(100 - a - 3)/100} × {(100 - a + 3)/100} = 2268/2800 or, (97 - a) × (103 - a) = (2268/2800) × 100 × 100 or, 97 × 103 - 97a - 103a + a² = 8112 or, a² - 200a + 9991 - 8112 = 0 or, a² - 200a + 1879 = 0 or, a² - 10a - 190a + 1879 = 0 or, a × (a - 10) - 187 × (a - 10) = 10 or, (a - 10) × (a - 187) = 10 So, a = 10 or a = 187 But, a = 187 is not possible because the discount cannot be more than 100%. Therefore, a = 10