Question

five times the cost price of a notebook is equal to four times the selling price of The notebook if the selling price is rupees 5 more than the cost price then find both the CP and SP of notebook​

Answer 1

$\begin{gathered}\begin{gathered}\bf \: Given - \begin{cases} &\sf{Selling \: Price \: = \: 5 + Cost \: Price} \\ &\sf{5 \: Cost \: Price = 4 \: Selling \: Price} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \: To\:find - \begin{cases} &\sf{Selling \: Price \: of \: notebook} \\ &\sf{Cost \: Price \: of \: notebook}  \end{cases}\end{gathered}\end{gathered}$

$\large\underline{\bold{Solution-}}$

Given that

• Selling Price is Rs 5 more than the Cost Price.

So,

$\begin{gathered}\begin{gathered}\bf \: Let - \begin{cases} &\sf{Cost \: Price \: of \: notebook= \: Rs \: x} \\ &\sf{Selling \: Price \: of \: notebook = \: Rs \: x + 5} \end{cases}\end{gathered}\end{gathered}$

Now,

$\large \bull \underline{\tt \:{ According  \: to  \: statement }}$

$\rm :\longmapsto\:5 \times Cost \: Price \: = \: 4 \times \: Selling Price$

$\rm :\longmapsto\:5 \times x = 4 \times (x + 5)$

$\rm :\longmapsto\:5x = 4x + 20$

$\rm :\implies\: \: \boxed{ \bf \:x \: = \: 20 }$

$\begin{gathered}\begin{gathered}\bf \: Hence- \begin{cases} &\sf{Cost \: Price \: of \: notebook= \: Rs \: 20} \\ &\sf{Selling \: Price \: of \: notebook = \: 20 + 5 = Rs \: 25} \end{cases}\end{gathered}\end{gathered}$

Basic Concept :-

• How to represent Systems of Linear Equation from Word Problems

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.