Question

The owner of an electronics shop charges his customer 22% more than the cost price. If a customer paid Rs.10980 for a DVD player then what was the cost price of a DVD player?
A) Rs.8000
B) Rs.8800
C) Rs.9500
D) Rs.9000

Answer 1

Hint: Here we will first let the cost price to be x and then form a linear equation with the help of the given information and then find the value of \[x\] to get the cost price.
The selling price is the price at which an article is sold while the cost price is the price at which the article is bought.
A linear equation in one variable is an equation in which the highest power of the variable is one and has one variable only.

Complete step by step solution:
Let the cost price of the DVD player be \[x\]
Now since it is given that the selling price is 22% more than the cost price
Hence the selling price is given by:-
\[{\text{selling price}} = {\text{cost price}} + {\text{22% of cost price}}\]
Now since it is given that the selling price of the DVD player is Rs. 10980
Hence putting in the values we get:-
\[\Rightarrow 10980 = x + 22\% {\text{ of }}x \]
On simplification of the above equation, we get
$\Rightarrow 10980 = x + \dfrac{{22}}{{100}}x $
On further calculations,
$\Rightarrow 10980 = x + \dfrac{{11}}{{50}}x $
Solving for \[x\] we get:-
\[\Rightarrow \dfrac{{50x + 11x}}{{50}} = 10980 \]
On simplification of the above equation, we get
$\Rightarrow \dfrac{{61x}}{{50}} = 10980$
On further simplification,
$\Rightarrow 61x = 50 \times 10980 $
$\Rightarrow 61x = 549000 $
Dividing the whole equation by 61 to get the value of \[x\]:-
\[\Rightarrow x = \dfrac{{549000}}{{61}} \]
 $\Rightarrow x = 9000 $

$\therefore$ The cost price of the DVD player is Rs.9000. Hence option (D) is the correct option.

Note:
A student might make mistakes in forming the linear equation.
So one should first understand he given information first and then make the equation using following equation:-
\[{\text{selling price}} = {\text{cost price}} + {\text{22% of cost price}}\]