By selling an article for rs.17,a shopkeeper losses 15%. At what price should he sell it to gain 15% ?
To find the selling price at which the shopkeeper would gain 15% profit, we need to determine the cost price of the article and then calculate the new selling price using the profit percentage.
Let's start by understanding the meaning of a 15% loss.
A 15% loss means that the selling price is 85% of the cost price. In other words, the article was sold for 85% of its cost price.
We can set up the following equation based on this information:
Selling Price = Cost Price - Loss
Now, let's denote the cost price as CP and the selling price as SP:
SP = 85% of CP
SP = (85/100) * CP
SP = 0.85 * CP
Given that the selling price is Rs. 17, we can substitute this value into the equation:
17 = 0.85 * CP
To find CP, we need to isolate it on one side of the equation. Divide both sides by 0.85:
17/0.85 = CP
Therefore, the cost price (CP) is Rs. 20.
Now, to calculate the selling price to gain a 15% profit, we will use the formula:
Selling Price = Cost Price + Profit
Let's denote the new selling price as SP_new, the cost price as CP, and the profit as P:
SP_new = CP + P
Given that the profit is 15%, we can calculate the profit amount by finding 15% of the cost price:
P = 15% of CP
P = (15/100) * CP
P = 0.15 * CP
Substituting the values:
SP_new = CP + 0.15 * CP
SP_new = 1.15 * CP
Substituting the value of the cost price (CP = Rs. 20):
SP_new = 1.15 * 20
SP_new = Rs. 23
Therefore, to gain a 15% profit, the shopkeeper should sell the article for Rs. 23.
0.85x = 17
x = 20