Question

13. The selling price of 10 articles is equal to the cost price of 11 articles. Find the gain per cent. ​

Answer 1

The Gain Percentage = 10 %

Step-by-step explanation:

From Given, it is said that,

Selling Price of 10 Articles = Cost Price of 11 Articles.

From this, we can say that, The Cost of Selling 10 Articles is equal to the Cost of 11 Articles.

According to the question,

Let the Price of an Article be $'x'$

Cost price of 10 Articles = $\sf{10\:\times\:x\:=\:10x}$

And Selling Price of 11 Articles = $\sf{11\:\times\:x\:=\:11x}$

Formulas Needed,

${\boxed{\bullet\:{Profit\:=\:Selling Price\:-\:Cost Price}}}$

${\boxed{\bullet\:{Profit\:Percent\:=\:{\dfrac{Profit}{Cost\:Price}}\:\times\:100}}}$

Finding Profit, Using Formula,

$\boxed{Profit\:=\:Selling Price\:-\:Cost Price}$

$\implies\sf{Profit\:=\:11x\:-\:10x}$

$\implies\sf{Profit\:=\:1x}$

Profit Percentage,

$\boxed{Profit\:Percent\:=\:{\dfrac{Profit}{Cost\:Price}}\:\times\:100}$

$\implies\sf{Profit\:Percent\:=\:{\dfrac{1x}{10x}}\:\times\:100}$

$\implies\sf{Profit\:Percent\:=\:{\cancel{{\dfrac{1x}{10x}}}}\:\times\:100}$

$\implies\sf{Profit\:Percent\:=\:10}$ %

Hence, The Gain Percentage = 10 %

Answer 2

To find:

$\to$The gain per cent. ​

Information given in the question:

• The selling price of 10 articles is equal to the cost price of 11 articles

Solution:

Let,The cost price of the 11 articles be $x$ rs

$\to$(Cost price of 11 articles) = (Selling price of 10 articles)

So,The selling price of 10 articles = $x$ rs

Therefore,

$\to$The cost price of 1 article = $\frac{x}{11}$ rs

$\to$The selling price of 1 article = $\frac{x}{10}$ rs

Using formula:

$\to$Profit amount = (Selling Price - Cost Price)

Thus,

$\to$The Profit amount =

$(\frac{x}{10} - \frac{x}{11} )rs\\\\=(\frac{11x - 10x}{110} )rs\\\\=(\frac{x}{110} )rs$

Using formula:

$\to$Gain Percent = $\frac{Profit Amount * 100}{Cost Price}$

So,The gain percent=

$(\frac{x}{110} * \frac{11}{x} * 100)$ %

$=(\frac{100}{10} )$ %

$= 10$ %

Answer:

The gain percent = $10$ %