A shopkeeper allows 18% discount on the marked price of an article and still makes a profit of 23% . If he gains Rs 1840 on the sale of the article, then what is the marked price of the article?

 

Correct option is C

​Given:

Discount = 18%

Profit = 23%

Profit Amount = Rs. 1840

Formula Used:

Profit formula: $$\text{Profit} = \text{S.P.} - \text{C.P.}$$​​

Selling Price after discount:

$$\text{S.P.} = \text{M.P.} \times \left( 1 - \frac{\text{Discount Percentage}}{100} \right)$$​​

Relationship between S.P. and C.P.:

$$\text{S.P.} = \text{C.P.} \times \left( 1 + \frac{\text{Profit Percentage}}{100} \right)$$​​

Solution:

Cost Price (C.P.) = x

Marked Price (M.P.) = y

From the profit formula:

​$$\text{S.P.} = x \times \left( 1 + \frac{23}{100} \right) = x \times 1.23$$​​

​$$1840 = x \times 0.23 \quad \Rightarrow \quad x = \frac{1840}{0.23} = 8000$$​​

Selling Price after discount:

​$$\text{S.P.} = y \times \left( 1 - \frac{18}{100} \right) = y \times 0.82$$​​

Equating S.P. values:

​$$x \times 1.23 = y \times 0.82 \quad \Rightarrow \quad 8000 \times 1.23 = y \times 0.82$$​​

​$$y = \frac {8000×1.23}{0.82} = 12000$$​​