Question

A shopkeeper sold an article for rupees 450 at loss of 10% at what price should he sell so as to gain 10%?

Answer 1

Because the $450 price is discounted 10% from the original, that means that it is 90% or 9/10 of the original price.

In order to find the original prince, we need to divide $450 by 9/10, or, in other words, multiply it by its opposite (reciprocal) like so:

450 x (10/9) = 450 x 1/9 x 10 = 500, so $500.

A 25% profit represents 1/4 of the price, so that’s:

500 x 1/4 = 125, so $125.

Now, how much money does he make after the sale? Although the overall price of the item went down by 10%, the amount of money that the shopkeeper has to spend to buy the item in the first place and on overhead stays the same.

That means that the difference between the original price and the discounted price all comes from the shopkeeper’s profit. That is:

500 - 450 = 50, so $50.

Then, the profit would be:

125 - 50 = 75, so $75.

The percentage profit, by definition, is amount profit/price, making it:

75/450 = 1/6 = .166666…. (sixes repeating forever), simplifying to around 16.7%.

Hope this helps :)