If the cost price of 20 articles is equal to the selling price of 25 article,what is the percentage profit or loss made? [Full Solution]
Answers
Given,
The cost price of 20 articles is equal to the selling price of 25 articles.
To find,
The percentage profit or loss made.
Solution,
We can simply solve this mathematical problem using the following process:
Let us assume that the cost price and selling price of each article is Rs. x and Rs. y, respectively.
Mathematically,
(a) (Selling price) = (cost price) + (profit earned) = (cost price) - (loss amount)
(b) profit/loss percentage = (profit earned/loss amount)/(cost price)×100
{Statement-1}
Now, according to the question;
The total cost price of 20 articles
= 20 × (cost price of each article)
= 20 × Rs. x
= Rs. 20x
And, the selling price of 25 articles
= 25 × (selling price of each article)
= 25 × Rs. y
= Rs. 25y
Now, according to the question;
The cost price of 20 articles = the selling price of 25 articles
=> Rs. 20x = Rs. 25y
=> 20x = 25y
=> 4x = 5y
=> y/x = 4/5 {Equation-1}
=> y < x
=> (selling price of each article) < (cost price of each article)
=> the articles are sold at a loss
Now, the total loss amount for each article sold
= (cost price of each article) - (selling price of each article)
{according to statement-1}
= Rs. x - Rs. y
= Rs. (x-y)
Now,
The loss percentage
= (loss amount)/(cost price)×100
= {Rs. (x-y)}/ Rs. x × 100
= (x-y)/x × 100
= {1-(y/x)} × 100
{according to equation-1}
= {1-(4/5)} × 100
= (5-4)/5 × 100
= 1/5 × 100 = 20%
Hence, the articles are sold at a loss of 20%.