Question

Raman sells two wrist watches for \[Rs.1200\] each. On one watch he gains \[20\%\] and on the other watch he loses \[20\%\]. What are the cost prices of each and what is his total gain or loss percentage?

Answer 1

Hint: Firstly, we must find the cost price of each wrist watch with respect to the given selling price. Then we must calculate the total cost price and the total selling price to determine if Raman had a loss or gain on selling his watches. After finding the respective values we are supposed to find the percentage of the loss or gain.

Complete step by step answer:
Now let us learn about selling price and cost price. The price at which a good is being bought is considered as cost price. In the same way, the price at which the goods are being sold is called the selling price. While comparing the cost price and selling price, if the cost price is greater than the selling price, then loss occurs. If the selling price is greater than the cost price, then gain or profit occurs.
Now let us solve the given problem.
Let us find the cost price of one watch on which he gained \[20\%\].
We know that, selling price is \[Rs.1200\]
Let the cost price be \[x\].
Now let us calculate the cost price, we get
\[\begin{align}
  & \Rightarrow 1200=x+\dfrac{20}{100}\left( x \right) \\
 & \Rightarrow 1200=x+\dfrac{x}{5}=\dfrac{6x}{5} \\
 & \Rightarrow 6000=6x \\
 & \Rightarrow x=1000 \\
\end{align}\]
\[\therefore \] The cost price of the watch on which he gains \[20\%\] is \[Rs.1000\]
Let us find out the cost price of the watch on which he loses \[20\%\].
Selling price is \[Rs.1200\]
Let the cost price be y.
Now let us calculate the cost price, we get
\[\begin{align}
  & \Rightarrow 1200=y-\dfrac{20}{100}\left( x \right) \\
 & \Rightarrow 1200=y-\dfrac{y}{5}=\dfrac{4y}{5} \\
 & \Rightarrow 6000=4y \\
 & \Rightarrow x=1500 \\
\end{align}\]
\[\therefore \] The cost price of the watch on which he loses \[20\%\] is \[Rs.1500\].
Now let us calculate the total cost price and the total selling price.
Total cost price of both the watches is \[1500+1000=2500\]
Total selling prices of both the watches is \[1200+1200=2400\]
Upon comparing the cost price and selling price we can see that the cost price of both watches is greater than the cost price of both watches.
If the cost price is greater, then loss occurs on the total transaction.
Now let us calculate the loss percentage.
\[\begin{align}
  & Loss\%=\dfrac{2500-2400}{2500}\times 100 \\
 & \Rightarrow \dfrac{100}{2500}\times 100=4\% \\
\end{align}\]
\[\therefore \] Raman gets a loss of \[4\%\] on selling both the watches .

Note: We must have a note that the cost price or the selling price can never be negative. In order to remove the negative nature, we will be applying mod to the value which converts into positive. We can apply this loss or gain percent in everyday life to calculate them.