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Thirty articles are bought for 450 each . If one third of these sold at a 6% loss , at what price must each of the remaining articles be sold in order to make a profit of 10% in whole.

Last updated date: 22nd Feb 2024
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IVSAT 2024
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Hint: We know that the price of each article is 450 each, first we will calculate the total price of 30 articles. Then we will find the price at which we should sell the 30 articles so that total profit will be 10% . Then we will find the sold price of one third of articles, and the sold price of remaining articles.

Complete step by step solution:
Price of each article is 450, so the total price of 30 article is equal to $30\times 450$ = 13500
One third of article sold at price 6% loss , price of 10 articles is 4500
So sold price of 10 articles is equal to $4500\times \dfrac{94}{100}=4230$
In order to make 10% the total sold price should be equal to $13500\times \dfrac{110}{100}=14850$
So, sold price of remaining two third of article is $14850 – 4230 = 10620$
So the sold price of 20 articles is equal to $10620$.

So sold price of each article from remaining is equal to $\dfrac{10620}{20}=531$.

Note: If the price of an item is equal to a and we make a profit of x% by selling it , then the sold price of the item is equal to $\dfrac{a\left( 100+x \right)}{100}$ and in the other way if the sold price is equal to a and the profit is x% , then the original price of the item is $\dfrac{a\left( 100 \right)}{100+x}$