Calculate Cost Price Using Markup and Discount
Let the Cost Price (CP) of the article be represented by \(C\).
Markup Calculation
The shopkeeper marks the article 30% above the cost price. The Marked Price (MP) is calculated as:
\(MP = CP + (30\% \text{ of } CP)\)
\(MP = C + 0.30C\)
\(MP = 1.30C\)
Discount Application
A discount of 20% is given on the Marked Price. The Selling Price (SP) is calculated as:
\(SP = MP - (20\% \text{ of } MP)\)
\(SP = MP \times (1 - 0.20)\)
\(SP = 0.80 \times MP\)
Selling Price in Terms of Cost Price
Substitute the expression for MP into the SP equation:
\(SP = 0.80 \times (1.30C)\)
\(SP = 1.04C\)
Profit Calculation
The profit made is ₹32. Profit is the difference between Selling Price and Cost Price:
\(Profit = SP - CP\)
\(₹32 = 1.04C - C\)
\(₹32 = 0.04C\)
Find the Cost Price
Solve for \(C\):
\(C = \frac{₹32}{0.04}\)
\(C = \frac{3200}{4}\)
\(C = ₹800\)
Therefore, the cost price of the article is ₹800.
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