Question

A dealer buys an old cooler listed at Rs.950 and gets a discount of 10%. He spends Rs 45 for its repair . If he sells the cooler at a profit of 25%, then the selling price of the cooler is
A.Rs. 1125
B.Rs. 1215
C.Rs. 1251
D.Rs. 1512

Answer 1

Hint: The cost price /selling price of the cooler can be calculated by using the formula when he sold with profit percentage is ${\text{C}}{\text{.P}}{\text{. = }}\dfrac{{{\text{S}}{\text{.P}} \times 100}}{{100 + {\text{ profit % }}}}$Where S.P is the selling price and C.P is the cost price. First from the question, we need to find the Cost price and then we need to add the cost for repairs which will give the net cost price. This Net Cost price is used to calculate the selling price. $\therefore {\text{S}}{\text{.P}}{\text{. = }}\dfrac{{100 + {\text{ profit % }}}}{{100}} \times {\text{C}}{\text{.P}}{\text{.}}$

Complete step-by-step answer:
Given, Dealer buys a cooler listed Rs. 950 and gets a discount of 10%
That is,
Cost Price of the cooler = Rs.950 – (10% of Rs.950)
$\begin{gathered}
   \Rightarrow 950 - \left( {\dfrac{{10}}{{100}} \times 950} \right) \\
   \Rightarrow 950 - 95 = {\text{Rs}}{\text{.855}} \\
\end{gathered} $
Therefore, Cost price of cooler = Rs. 855
Given repair cost for the cooler = Rs.45
Net cost price can be calculated by adding repair cost to the cost price of the cooler
Therefore, Net Cost Price = Rs. 855 + Rs. 45 =Rs. 900
Profit percentage while selling the cooler = 25%
We know that, Cost price can be calculated by using the below formula,
${\text{C}}{\text{.P}}{\text{. = }}\dfrac{{{\text{S}}{\text{.P}} \times 100}}{{100 + {\text{ profit % }}}}$
From this formula we can get the selling price formula.
$\therefore {\text{S}}{\text{.P}}{\text{. = }}\dfrac{{100 + {\text{ profit % }}}}{{100}} \times {\text{C}}{\text{.P}}{\text{.}}$
Where, Profit % = 15%
C.P = Rs. 900
$\therefore {\text{S}}{\text{.P}}{\text{. = Rs}}{\text{.}}\dfrac{{100 + 25}}{{100}} \times 900$
${\text{S}}{\text{.P}}{\text{. = }}\dfrac{{900 \times 125}}{{100}} = {\text{Rs}}{\text{. }}1125$
Therefore, Selling Price = Rs. 1125

Note: In the above problem, we have been given the profit percentage. Instead if it was loss percentage, we need to use ${\text{C}}{\text{.P}}{\text{. = }}\dfrac{{{\text{S}}{\text{.P}} \times 100}}{{100 - {\text{loss % }}}}$. From this formula we need to convert to calculate the selling price. Then the selling price formula will be ${\text{S}}{\text{.P}}{\text{. = }}\dfrac{{100 - {\text{loss % }}}}{{100}} \times {\text{C}}{\text{.P}}$. From these formulae we can calculate the loss percentage/ profit percentage when we were given both the selling price and cost price.