Question

Find the selling price when \[CP=Rs.450\], profit =7%.

Answer 1

Hint: As we were given that the profit is equal to 7% when \[CP=Rs.450\]. Let us assume this as equation (1). Now we should find the amount of profit by using this C.P. We know that if the C.P of an item is x, then the profit percentage is equal to \[\dfrac{profit}{C.P}\times 100\]. We know that the difference between selling price and cost price is equal to profit. By using equation (1) and \[CP=Rs.450\], we can find the selling price.

Complete step-by-step answer:
Before solving the question, we should know about the definition of profit. If the difference of selling price and cost price is positive, then the profit is said to be obtained. If the difference of selling price and cost price is negative, then the loss is said to be obtained.
From the question, we were given that the cost price is Rs.450 and the profit is 7%.
We know that if the C.P of an item is x, then the profit percentage is equal to \[\dfrac{profit}{C.P}\times 100\].
\[\Rightarrow 7=\dfrac{\operatorname{Profit}}{450}\times 100\]
By using cross multiplication, we get
\[\begin{align}
  & \Rightarrow \text{Profit =Rs }\dfrac{7}{100}\left( 450 \right) \\
 & \Rightarrow \text{ Profit =Rs 37}\text{.5}.....\text{(1)} \\
\end{align}\]
So, it is clear that the profit is equal to Rs 37.5.
We know that the difference between selling price and cost price is equal to profit.
We know that the cost price is equal to Rs. 450.
\[\Rightarrow C.P=Rs450....(2)\]
Let us assume the cost price is equal to C.P.
Let us assume the selling price is equal to S.P.
\[\Rightarrow \text{Profit = S}\text{.P-C}\text{.P}.....\text{(3)}\]
To find S.P, we should substitute equation (1) and equation (2) in equation (3).
\[\begin{align}
  & \Rightarrow 37.5=S.P-450 \\
 & \Rightarrow S.P=Rs(450+37.5) \\
 & \Rightarrow S.P=Rs487.5 \\
\end{align}\]
So, it is clear that the selling price is equal to 487.5.

Note: Students should be careful while doing calculations. If a small mistake is made the result may go wrong. So, students may write the profit as the difference between selling price and cost price.
\[\begin{align}
  & \Rightarrow \text{Profit = C}\text{.P-S}\text{.P} \\
 & \Rightarrow \text{37}\text{.5 =450-S}\text{.P} \\
 & \Rightarrow \text{S}\text{.P=Rs(450-37}\text{.5)} \\
 & \Rightarrow S\text{.P=Rs (412}\text{.5)} \\
\end{align}\]
So, we get the selling price is equal to Rs 412.5. We know that this is a wrong answer.