Question

Ramrao bought a cupboard for Rs.4500 and sold it for Rs.4950. Shamrao bought a sewing machine for Rs.3500 and sold it for Rs.3920. Whose transaction was more profitable?

Answer 1

Hint: Find the profit earned by Ramrao and Shamrao individually using the cost price and selling price given, i.e., Profit = Selling Price – Cost Price. Consider x% and y% as the profit earned by Ramrao and Shamrao. Thus find the profit percentage by dividing profit by cost price. Then compare the profit percentage of Ramrao and Shamrao to find the most profitable among them.

Complete step-by-step answer:
Let us consider the first case of Ramrao, where he bought a cupboard for Rs.4500 and sold it for Rs.4950.
\[\therefore \]The cost price (CP) of the cupboard = Rs.4500.
The selling price (SP) of the cupboard = Rs.4950.
So from this we can understand that the selling price is more than the cost price, so there is a profit.
Profit is given by the difference of selling price and cost price.
Profit = selling price – cost price = Rs.4950 – Rs.4500 = Rs.450.
So, Ramrao made a profit of Rs.450 in this transaction.
Now let us take the second case of Shamrao where he bought a sewing machine for Rs.3500 and sold it for Rs.3920.
 \[\therefore \]The cost price (CP) of sewing machines = Rs.3500.
The selling price (SP) of sewing machine = Rs.3920.
So from this we can understand that the selling price is more than the cost price, and since there is a profit.
\[\therefore \]Profit = Selling price (SP) – cost price (CP)
               = Rs.3920 – Rs.3500
               =Rs.420.
So Shamrao made a profit of Rs.420.
Let x% be the Ramrao’s profit and y% be the Shamrao’s profit.
\[\dfrac{x}{100}\]=Profit/cost price\[=\dfrac{450}{4500}\].
\[\begin{align}
  & \dfrac{x}{100}\times 100=\dfrac{450}{4500}\times 100=10 \\
 & \Rightarrow x=10\\
\end{align}\]
\[\dfrac{y}{100}\times 100=\dfrac{420}{3500}\times 100\], Simplifying it we get,
\[\Rightarrow y=12%\]
So from this we can make out that Ramrao made a profit of 10% and Shamrao made a profit of 12% on a sewing machine.
Hence, Shamrao’s transaction was more profitable.

Note: Easiest way of solving it is to directly find profit percentage.
x = Profit/ CP\[=\left( \dfrac{SP-CP}{CP} \right)\times 100=\left( \dfrac{4950-4500}{4500} \right)\times 100=10%\].
Similarly, y = Profit/CP\[=\left( \dfrac{SP-CP}{CP} \right)\times 100=\left( \dfrac{3920-3500}{3500} \right)\times 100=12%\]