The marked price of an article is ₹492. The shopkeeper offers a discount of 39% on the purchase of the article. Thereby, he makes a profit of 22%. The cost price of the article is:

Correct option is D

Given:

Marked Price (MP) = ₹492

Discount Percentage = 39%

Profit Percentage = 22%

Formula Used:

​$$\text{Selling Price (SP)} = \text{MP} - \frac{\text{Discount Percentage} \times \text{MP}}{100}$$​​

​$$\text{SP} = \text{CP} + \frac{\text{Profit Percentage} \times \text{CP}}{100}$$​​

Solution:

SP = 492 - $$\frac{39 \times 492}{ 100}$$​​

SP = 492 - 191.88

SP = ₹300.12

SP = $$\text{CP} + \frac{22 \times \text{CP}}{100}$$​​

300.12 = $$\text{CP} \times \left( 1 + \frac{22}{100} \right)$$​​

300.12 = $$\text{CP} \times \left( \frac{122}{100} \right)$$​​

CP = $$\frac{30012 }{ 122}$$​​

CP = ₹246

The cost price of the article is ₹246.

Option (D) is right.

Alternate Method:

$$\frac{CP}{MP}=\frac{(100 - D\%)}{(100\pm P/L \%)}$$

$$\frac{CP}{492}=\frac {100-39}{100 +22}$$

​​​$$\frac{CP}{492}=\frac {61}{122}$$

CP =  $$\frac{492}{2}$$ = ₹246

Option (D) is right.​