On selling an article at successive discounts of 20% and 25% a dealer makes a net profit of 20%, Find the net profit per cent if the dealer sells the same article at a discount of 25%.
Answers
Let the selling price be x
Find the selling price after first 20% discount:
Discount = 20% of x = 0.2x
Price after discount = x - 0.2x = 0.8x
Find the selling price after second discount:
Discount = 25% of 0.8x = 0.25 x 0.8x = 0.2x
Price after discount = 0.8x - 0.2x = 0.6x
Find the selling price percentage:
Profit = 20%
Cost Price = 100%
Selling Price = Cost Price + Profit
Selling Price = 100 + 20 = 120%
Find the cost price:
Selling Price = 0.6x
Selling Price = 120%
120% = 0.6x
1% = 0.6x ÷ 120 = 0.005x
100% = 0.005x x 100 = 0.5x
Cost Price = 0.5x
Find the profit if the same article were sold at 25% discount:
25% Discount = 0.25x
Selling Price after discount = x - 0.25x = 0.75x
Profit = Selling Price - Cost Price
Profit = 0.75x - 0.5x = 0.25x
Find the profit percentage:
Profit Percentage = Profit / Cost Price x 100
Profit Percentage = ( 0.25x / 0.5x ) x 100 = 50%
Answer: The profit is 50%