Question

# By selling 20 articles, a person gains a CP of 5 articles. Find the profit % incurred by him.

Hint: For solving this type of question, first we will calculate the profit in terms of some unknown variable term and in the same variable term we will then compare with the cost price with the help of given values.

As we know that, $profit = S.P - C.P$
Where S.P= selling price and C.P= cost price.
Let the S.P of one article be S and the cost price of another article be C.
Total sale price $= 20S$
Total cost price $= 20C$
Net profit
$= S.P - C.P \\ = 20S - 20C \\$
It is given that net profit
$= 5C \\ \because 5C = 20S - 20C \\ \Rightarrow 25C = 20S \\ \Rightarrow \dfrac{S}{C} = \dfrac{{25}}{{20}} = \dfrac{5}{4} \\$
Thus, the relation between cost price and selling price is
$\dfrac{S}{C} = \dfrac{5}{4} \\ 4S = 5C \\ S = \dfrac{5}{4}C \\$
Profit percentage is
$= \dfrac{{S - C}}{C} \times 100 \\ = \dfrac{{\dfrac{5}{4}C - C}}{C} \times 100 \\ = \dfrac{{C\left( {5 - 4} \right)}}{{4C}} \times 100 \\ = \dfrac{{5 - 4}}{4} \times 100 = 25\% \\$
Hence, a total of 25% profit was made by the person.

Note: In this type of numerical, formulate equations from the given conditions and solve these equations in such a manner to deduce one variable in terms of another. This problem can also be solved in another way by considering one unit of the given commodity and then proceeding further to find the cost price and profit of one unit. Eventually the profit percent on one unit will be overall profit percent.