Question

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%.

Answer 1

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%