A man sells an item at 25% profit. had he purchased it for rs. 300 less and sold it for rs.300 less then he would gain 30% profit find the initial cast price of the items.
Answers
Answer:
A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs.1050 less, he would have gained 30%. How do I find the cost price of the article?
Season to start anew.
Let x be the cost price of the article (the price at which he buys the article from the wholesaler).
Selling the article at a profit of 25% means that currently its price is 125100x . Had he bought it at 20% less, he would have done so at a cost price of
x−20100⋅x=80100x .
Adding 30% gain to that cost price in the hypothetical case would set the price at
80100x+30100⋅80100x
That price is 1,050 less than the current ( 125100x ), i.e., 125100x−1,050
Hence, we can now work out an equation, the solution of which would lead us to the current (actual) cost price:
80100x+30100⋅80100x=125100x−1,050
(hypothetical cost price + 30% of the hypothetical cost price = actual price - Rs.1,050)
80100x+310⋅810x=125100x−1,050
The right side of the equation is the amount that the hypothetical sale adds to the turnover; subtract that from the cost price to find the actual profit. Let us continue solving for x:
80100x+24100x=125100x−1,050
80x+24x=125x−105,000
21x=105,000
x=5,000
Therefore, the cost price of the article is Rs.5000 and the man sells it at Rs.6250 for a 25% profit of Rs.1250 per article sold.
It might be worth mentioning that if he had bought the article at a cost price of Rs.4000 (20% less) and sold it at a price of Rs.5200 for a 30% gain, the real profit would have been only Rs.1,185, which is 5.2% less than in the case where he sells it for 25% profit; since lowering the price of a high quality product increases the demand of it (all other factors being the same) – and, therefore, the volume of its sales – such an act would lead to more work for less money, i.e., depreciate the wage labour, basically depreciating the product itself… If the article is a product of high quality indeed, mind you. This can be, for example, due to mass producing it and making it available to more people, but it may also be a symptom of a dying product (one that is on its path towards disappearing from the market), or even a whole company.