Buying & Selling: Calculate Discount & Profit %

[chawki]

Homework Statement

A retailer buys a batch of 50 items of a product for 10 000 €. He then sets a price so that the
selling price is 80 % higher than the buying price. When there is 40 % left of the batch, the
retailer lowers the price and manages to sell off the rest for a reduced selling price of
171 €/item.

Homework Equations

a) Calculate the discount percentage relative to the initial selling price.
b) Calculate the profit percentage for the whole batch.
Give your answers with an accuracy of one decimal.

The Attempt at a Solution

Let's resume what he did.
he bought 50 items for 10000€ means 1 item for 200€
when he set the selling price, it was 200*1.80 = 360€ for one item.
60% out of 50 items were sold by 360€/item...that gives us 360*30items = 10800€.
40% that is 20 items were sold by 171€*20 = 3420€.

a)
the discount percentage relative to the initial selling price: is the discount from 200€/item to 171€/item
200€-----------100%
171€-----------x%
x% = 85.5%
The discount is 100%-85.5%= 14.5%

b)
the profit percentage for the whole batch (50 items) is 80%-14.5% = 65.5% ?
OR
10800€+3420€ = 14220€ for the whole batch
that's:
10000€-------100%
14220€-------y%
y% = 142.2%
the prfit percentage for the whole batch is 42.2% ?

 

[Dollydaggerxo]

"a) Calculate the discount percentage relative to the initial selling price."

does this not relate to the 360 dollars rather than the 200? as 200 is the buying price. Maybe I have just read it differently. Your working is correct though.

your part b looks correct too