Question

A shopkeeper earns a profit of 15 percent on selling a radio, whereas if he sold for 7360 less, he suffers a loss of 15 percent. What is the cost price for the shopkeeper?

Answer 1

Hint: Now the first condition is the shopkeeper earns a profit of 15 percent on selling a radio. Now assume CP to be x and SP to be y. Now we know that profit = SP – CP. Also profit percentage $\dfrac{profit}{CP}\times 100$ . Hence we find a relation between x and y. Now by second condition we have if he sold for 7360 less, he suffers a loss of 15 percent. Hence again we know Loss = SP – CP and loss percentage is given by $\dfrac{loss}{CP}\times 100$ hence we get a second equation in x and y solve the two equations to get x, that is the cost price.

Complete step by step answer:
Now we are given that the shopkeeper earns a profit of 15 percent on selling a radio.
Now let the cost price be x and the selling price be y.
Now we know that profit is given by $SP-CP$
Then the profit is y – x.
Now the profit percentage is given by $\dfrac{profit}{CP}\times 100$
Hence the profit percentage is $\dfrac{y-x}{x}\times 100$
Now we are given that the profit percentage is 15. Hence we get
$\dfrac{y-x}{x}\times 100=15$
Now dividing by 5 on both sides we get.
\[\begin{align}
  & \Rightarrow \dfrac{y-x}{x}\times 20=3 \\
 & \Rightarrow 20y-20x=3x \\
 & \Rightarrow 20y=20x+3x \\
 & \Rightarrow 20y=23x \\
 & \Rightarrow y=\dfrac{23x}{20}..........................\left( 1 \right) \\
\end{align}\]
Now if he sells at 7360 less then he suffers a loss of 15 percent.
Now the old selling price is y.
Hence new selling price will be y – 7360
Now we know that Loss = CP – SP.
Now CP was x.
Hence the loss is equal to x – (y – 7360)
Loss = x – y + 7360
Now the loss percentage is given by $\dfrac{loss}{CP}\times 100$
Hence the profit percentage is $\dfrac{x-y+7360}{x}\times 100$
Now we are given that the profit percentage is 15. Hence we get
$\dfrac{x-y+7360}{x}\times 100=15$
Dividing by 5 and multiplying by x we get.
$\left( x-y+7360 \right)\times 20=3x$
$\begin{align}
  & \Rightarrow 20\left( x-y+7360 \right)=3x \\
 & \Rightarrow 20x-20y+147200=3x \\
\end{align}$
Rearranging terms we get
$20x-20y-3x=-147200$
$17x-20y=-147200$
Now from equation (1) we get
\[\begin{align}
  & 17x-20\left( \dfrac{23x}{20} \right)=-147200 \\
 & \Rightarrow 17x-\left( 23x \right)=-147200 \\
 & \Rightarrow -6x=-147200 \\
\end{align}\]
Dividing the whole equation by 6 we get x = 24533.33

Hence the CP was Rs. 24533.33

Note: Note that if there is a loss SP < CP hence we get loss = CP – SP and if there is profit then CP < SP hence we get profit = SP – CP.