Question

A trader sold an article at a loss of $5\%$ but when he increased the selling price by $\mathrm{Rs}65$. He gained $3.33\%$ on the cost price. If he sells the same article at $\mathrm{Rs}936$, what is the profit percentage?

Answer 1

Stetp 1. Calculate Actual Cost Price.

Let $\mathrm{Rs}.100$ be the cost price of the article.

When A trader has a loss of $5\%$, the selling price is calculated as follow:

$$\begin{gathered} \mathrm{S}.\mathrm{P}.=100-5\%\mathrm{of}\mathrm{C}.\mathrm{P}. \\ \Rightarrow \mathrm{S}.\mathrm{P}.=100-5 \\ \Rightarrow \mathrm{S}.\mathrm{P}=\mathrm{Rs}.95 \end{gathered}$$

After the increase$\left(\mathrm{by}x\right)$ in selling price traders gained a profit of $3.33\%$.

$$\begin{gathered} \mathrm{New}\mathrm{S}.\mathrm{P}.=\mathrm{C}.\mathrm{P}+3.33\%\mathrm{of}\mathrm{C}.\mathrm{P}. \\ \Rightarrow \mathrm{New}\mathrm{S}.\mathrm{P}.=100+3.33\%\mathrm{of}100 \\ \Rightarrow \mathrm{New}\mathrm{S}.\mathrm{P}.=\mathrm{Rs}.103.33 \end{gathered}$$

Total change in Selling price is when C.P. is assumed $\mathrm{Rs}.100$:

$$\begin{gathered} \mathrm{Change}\mathrm{in}\mathrm{S}.\mathrm{P}.=\mathrm{New}\mathrm{S}.\mathrm{P}.-\mathrm{S}.\mathrm{P}. \\ =\mathrm{Rs}.8.33 \end{gathered}$$

Also given that the actual increment in selling price is $\mathrm{Rs}.65$. for actual cost price.

Calculate the Actual Cost price:

$$\begin{gathered} \frac{\mathrm{Assumed}\mathrm{C}.\mathrm{P}}{\mathrm{Change}\mathrm{in}\mathrm{S}.\mathrm{P}\mathrm{when}\mathrm{C}.\mathrm{P}.\mathrm{is}\mathrm{assumed}}=\frac{\mathrm{Actual}\mathrm{C}.\mathrm{P}}{\mathrm{Actial}\mathrm{change}} \\ \Rightarrow \frac{\mathrm{Rs}.100}{\mathrm{Rs}.8.33}=\frac{\mathrm{Actual}\mathrm{C}.\mathrm{P}}{\mathrm{Rs}.65} \\ \Rightarrow \mathrm{Actual}\mathrm{C}.\mathrm{P}=\frac{\mathrm{Rs}.100}{\mathrm{Rs}.8.33}\times \mathrm{Rs}.65 \\ \Rightarrow \mathrm{Actual}\mathrm{C}.\mathrm{P}=\mathrm{Rs}.780.31 \end{gathered}$$

So, the Actual cost price $\mathrm{Rs}.780.31$

Step 2. Calculate profit, if S.P. is increased to $\mathrm{Rs}.936$

Determine the percentage change for $\mathrm{Rs}.936$:

$$\begin{gathered} \mathrm{Profit}\%=\frac{\mathrm{S}.\mathrm{P}.-\mathrm{Actual}\mathrm{C}.\mathrm{P}}{\mathrm{Actual}\mathrm{C}.\mathrm{P}}\times 100 \\ \Rightarrow \mathrm{Profit}\%=\frac{936-780.31}{780.31}\times 100 \\ \Rightarrow \mathrm{Profit}\%=\frac{155.68}{780.31}\times 100 \\ \Rightarrow \mathrm{Profit}\%=19.995\%\simeq 20\% \end{gathered}$$

Hence, the profit percentage is $20\%$.