The bar graph given below shows the discount percentage given and profit/loss percentage earned by shopkeeper on 5 different articles (P , Q, R, S and T) .
Note: negative sign shows the loss percentage.

On article R, if there is an additional discount of 10% is offered, the profit earned by him would be Rs.42, find the cost price of article R?

The correct answer is Rs.525.


From the given bar graph, we can observe the following data for article R:
• Discount percentage offered = 10%
• Profit percentage earned = 20%

Let the cost price of article R be represented as $\mathrm{CP}$.

Initially, the profit earned on article R is 20%. Therefore, the initial selling price (${\mathrm{SP}}_1$) in terms of $\mathrm{CP}$ is calculated as:

${\mathrm{SP}}_1=\mathrm{CP}\times \left(1+\frac{20}{100}\right)$

${\mathrm{SP}}_1=1.20\times \mathrm{CP}$

When an additional discount of 10% is offered on article R, the new selling price (${\mathrm{SP}}_2$) will be 90% of the initial selling price (${\mathrm{SP}}_1$):

${\mathrm{SP}}_2={\mathrm{SP}}_1\times \left(1-\frac{10}{100}\right)$

Substituting ${\mathrm{SP}}_1=1.20\times \mathrm{CP}$ into the equation:

${\mathrm{SP}}_2=\left(1.20\times \mathrm{CP}\right)\times 0.90$

${\mathrm{SP}}_2=1.08\times \mathrm{CP}$

The new profit earned with this revised selling price is given by:

$\text{New Profit}={\mathrm{SP}}_2-\mathrm{CP}$

$\text{New Profit}=1.08\times \mathrm{CP}-\mathrm{CP}=0.08\times \mathrm{CP}$

According to the problem statement, the new profit earned is Rs.42:

$0.08\times \mathrm{CP}=42$

Solving for $\mathrm{CP}$:

$\mathrm{CP}=\frac{42}{0.08}=\frac{4200}{8}=525$

Hence, the cost price of article R is Rs.525.