The percentage profit earned by selling an article for Rs. 1920 is equ...
To solve this problem, let's assume the cost price of the article is Rs. x.
Given that the percentage profit earned by selling the article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280, we can write the following equation:
Profit% = Loss%
Profit% = (Selling Price - Cost Price) / Cost Price * 100
Loss% = (Cost Price - Selling Price) / Cost Price * 100
According to the given information, we have:
(Selling Price - Cost Price) / Cost Price * 100 = (Cost Price - Selling Price) / Cost Price * 100
Simplifying this equation, we get:
(Selling Price - Cost Price) = (Cost Price - Selling Price)
2 * Selling Price = 2 * Cost Price
Selling Price = Cost Price
This means that the selling price is equal to the cost price.
To find the selling price that will give a 25% profit, we need to calculate 125% of the cost price.
125% of x = 1.25x
Therefore, the article should be sold for 1.25 times the cost price to make a 25% profit.
Since the cost price is x, the selling price should be 1.25x.
To find the value of x, we can use the given information:
Rs. 1920 = 1.25x
Dividing both sides by 1.25, we get:
x = Rs. 1536
Therefore, the cost price of the article is Rs. 1536.
To make a 25% profit, the selling price should be:
1.25 * Rs. 1536 = Rs. 1920
So, the correct option is a) Rs. 2000.