A shopkeeper listed the price of goods at 30% above the cost price. He sells half the stock at this price, one fourth of the stock at a discount of 15% and the remaining at 30% discount. His overall profit is

Let number of items = 4 (for simplicity)

Let C.P. for each = $$100x$$

Markup = $$\frac{30}{100} * 100x = 30x$$

=> M.P. = $$100x+30x = 130x$$

For first 2 items, S.P. = $$130x*2 = 260x$$

For the next item, discount = 15% => $$\frac{15}{100} * 130x = 19.5x$$

=> S.P. for the next item = $$130x-19.5x = 110.5x$$

Discount for final item = 30% => $$\frac{30}{100} * 130x = 39x$$

=> S.P. for final item = $$130x-39x = 91x$$

=> Total S.P. for 4 items = $$260x+110.5x+91x = 461.5x$$

and Total C.P. for 4 items = $$4*100x = 400x$$

=> Profit = $$\frac{461.5x-400x}{400x}$$ * 100 = $$\frac{123}{8}$$

= 15$$\frac{3}{8}$$%