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

Last updated date: 19th Mar 2023

•

Total views: 307.2k

•

Views today: 8.85k

Answer

Verified

307.2k+ views

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.

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.

Recently Updated Pages

If abc are pthqth and rth terms of a GP then left fraccb class 11 maths JEE_Main

If the pthqth and rth term of a GP are abc respectively class 11 maths JEE_Main

If abcdare any four consecutive coefficients of any class 11 maths JEE_Main

If A1A2 are the two AMs between two numbers a and b class 11 maths JEE_Main

If pthqthrth and sth terms of an AP be in GP then p class 11 maths JEE_Main

One root of the equation cos x x + frac12 0 lies in class 11 maths JEE_Main

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?