A rice bag's selling price is 'x%' greater than its cost price and 'x%' less than its marked price. The gain proportion from selling the item would increase to 25% if the selling price of the rice bag was dropped by Rs. thirty. Determine the cost of the rice bag if the item has a marked price of Rs. 360 and 'x' is an integer.

Solution

ATQ, Marked price of the rice bag = Rs. 360 So, selling price of the rice bag = Rs. 360 × {(100 - x) /100} So, cost price of the rice bag = 360 × {(100 - x) /100} × {100/(100 + x) } = Rs. 360 × {(100 - x) /(100 + x) } ATQ; 360 × {(100 - x) /100} - 30 = 360 × {(100 - x) /(100 + x) } × 1.25 Or, 3 × {(100 - x) /25} - 1 = 15 × {(100 - x) /(100 + x) } Or, 300 - 3x - 25 = 375 × {(100 - x) /(100 + x) } Or, (275 - 3x) × (100 + x) = 375 × (100 - x) Or, 27500 + 275x - 300x - 3x² = 37500 - 375x Or, 3x² + 10000 - 350x = 0 Or, 3x2 - 150x - 200x + 10000 = 0 Or, 3x(x - 50) - 200(x - 50) = 0 Or, (3x - 200) (x - 50) = 0 So, x = 50 or x = (200/3) Since, x is an integer, x = 50 So, cost price of the rice bag = 360 × {(100 - 50) /(100 + 50) } = Rs.120