Question

A man sells two articles at the same selling price- one at 25% profit and another at a 25% loss. What is the overall profit or loss percentage?
A. 10%
B. 5%
C. 6.25%
D. 12.5%

Answer 1

Hint: When an article is sold at a price higher to its cost price this is known as a profit and if the article is sold at a price lower than its cost price is known as loss. Generally Cost price is denoted as (C.P) whereas selling price is denoted by (S.P).
The Profit and Loss formula is used to find the price of the product or to predict the price at which the product must be sold to gain a profit.
Profit (P) =Selling price (SP)–Cost price (CP)
Loss (L) = Cost price (CP) –Selling price (SP)
When the Profit on a product is calculated in terms of percentage then it is known as profit percentage and in case of loss, it is known as loss percentage.

Complete step by step solution:
As mentioned the selling price for both the articles are hence let us consider that the selling price of article\[1\] =Selling price of article \[2\] be \[x\].
Now for the article \[1\] where the seller got a 25% profit on cost price CP is given as:
\[
  P = \dfrac{{SP - CP}}{{CP}} \times 100 \\
  25 = \dfrac{{x - CP}}{{CP}} \times 100 \\
  \dfrac{x}{{CP}} - 1 = 0.25 \\
  \dfrac{x}{{CP}} = 1.25 \\
  CP = \dfrac{x}{{1.25}} \\
 \]
For the article where the seller got a 25% profit, the cost price CP is \[\dfrac{x}{{1.25}}\]
Now for the article 2 where the seller got a 25% loss on cost price CP is given as:
\[
  P = \dfrac{{CP' - SP}}{{CP'}} \times 100 \\
  25 = \dfrac{{CP' - x}}{{CP'}} \times 100 \\
  1 - \dfrac{x}{{CP'}} = 0.25 \\
  \dfrac{x}{{CP'}} = 0.75 \\
  CP' = \dfrac{x}{{0.75}} \\
 \]
For the article where the seller got a 25% loss the cost price is \[\dfrac{x}{{0.75}}\]
Now, the total selling price of the two articles is \[S{P_T} = 2x\].
The total cost price for both the article:
\[
  C{P_T} = \dfrac{x}{{1.25}} + \dfrac{x}{{0.75}} \\
   = \dfrac{{100x}}{{125}} + \dfrac{{100x}}{{75}} \\
   = 100x\left( {\dfrac{{3 + 5}}{{375}}} \right) \\
   = 100x \times \dfrac{8}{{375}} \\
   = 2.13x \\
 \]
After combining both the articles’ prices we can see the seller got the loss on two articles as $ C{P_T} > S{P_T} $.
Hence,
\[
  Loss\% = \dfrac{{C{P_T} - S{P_T}}}{{C{P_T}}} \times 100 \\
   = \dfrac{{2.13x - 2x}}{{2x}} \times 100 \\
   = \dfrac{{0.13x}}{{2x}} \times 100 \\
   = \dfrac{{0.13}}{2} \times 100 \\
   = 6.5\% \\
 \]
Hence, there will be an overall loss percent of 6.5%.

Note: It is to be noted here that many a time, the marked price has been given in the question instead of selling price. So, be careful while reading the question as the marked price is the price which has been marked on the product by the seller but the selling price is the price of the product which the seller actually gets for the product after discount.