# A trader fixed the selling prices of goods at 30% above the cost price. He sells half of the stock at this price, one quarter of his stock at a discount of 15% on the original selling price and the rest at a discount of 30% on the original selling price. Find the gain percent altogether?

2
by gcbanerjee

2015-04-26T17:17:26+05:30

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Let the cost of making all the stock is 1,
then selling price = 1.3

Half of the stock was sold at original selling price, so sales money on half of the stock is :
1.3*1/2

One quarter of the stock was sold at a discount of 15% of selling price, which means it was sold at 85% of original selling price :
0.85*1.3*1/4

Remaining one quarter of the stock was sold at a discount of 30% of selling price, which means it was sold at 70% of original selling price :
0.7*1.3*1/4

Add them up to get the total sales money :
Total sales money = 1.3*1/2 + 0.85*1.3*1/4 + 0.7*1.3*1/4
= 1.15375

Subtract the cost price 1 from this to get the profit :
Profit = 1.15375 - 1 = 0.15375

Since the cost price is assumed to be unity, the profit is
One quarter of the stock was sold at a discount of 15% of selling price :
0.85*1.3*1/4
how 0.85?
good question, discount = 15% means he must have sold the stock at 85% of selling price, yes?
2015-04-26T21:09:40+05:30

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Let the cost price be CP.
Selling price : SP = SP + 30% SP = 1.30 CP

revenue from 1/2 stock sold at SP = 1/2 * SP

15% discount on SP = 15% SP = 0.15 * SP
Selling price after 15% discount =  1 - 0.15 SP = 0.85 SP
revenue from 1/4 stock sold at 15% = 1/4 *  0.85 * SP

selling price of the rest 1/4 of stock = (100-30)/100 SP  = 0.70 SP
revenue from the rest 1/4 of stock = 1/4 * 0.70 SP

total revenue = SP (1/2 + 0.85 / 4 + 0.70 / 4 ) = 0.8875 SP
= 0.8875 * 1.30 CP = 1.15375 CP

Gain %  = [ 1.15375 CP - CP ] / CP *100  = 15.375%