Calculating Original Cost Price
Let the original cost price (CP) be denoted by '\(CP\)' and the original selling price (SP) be denoted by '\(SP\)'.
Initial Scenario
The article is sold at a profit of 38%. The relationship between SP and CP is:
\( SP = CP + 0.38 \times CP = 1.38 \times CP \)
Modified Scenario
The cost price is increased by ₹68, and the selling price is reduced by ₹54.
- New Cost Price: \(CP_{new} = CP + 68\)
- New Selling Price: \(SP_{new} = SP - 54\)
The new profit is 37.5% (or 0.375).
The relationship for the new scenario is:
\( SP_{new} = CP_{new} + 0.375 \times CP_{new} = 1.375 \times CP_{new} \)
Setting up the Equation
Substitute the expressions for \(SP_{new}\) and \(CP_{new}\):
\( SP - 54 = 1.375 \times (CP + 68) \)
Now, substitute the expression for the original \(SP\) (\(SP = 1.38 \times CP\)):
\( (1.38 \times CP) - 54 = 1.375 \times (CP + 68) \)
Solving for Cost Price (CP)
- Expand the right side of the equation:
\( 1.38 \times CP - 54 = (1.375 \times CP) + (1.375 \times 68) \)
\( 1.38 \times CP - 54 = 1.375 \times CP + 93.5 \)
- Isolate the terms with \(CP\) on one side:
\( 1.38 \times CP - 1.375 \times CP = 93.5 + 54 \)
\( 0.005 \times CP = 147.5 \)
- Calculate the original \(CP\):
\( CP = \frac{147.5}{0.005} \)
\( CP = \frac{147500}{5} \)
\( CP = 29500 \)
The original cost price of the article is ₹29,500.
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