Calculating Marked Price from Selling Price and Discounts
We are given the final Selling Price (SP) and two successive discounts. We need to find the Marked Price (MP).
The formula for calculating Selling Price after successive discounts is:
\( SP = MP \times (1 - d_1) \times (1 - d_2) \)
Given values:
- \(SP = ₹430.5\)
- First discount (\(d_1\)) = 70% or 0.70
- Second discount (\(d_2\)) = 75% or 0.75
Substitute the values into the formula:
\( 430.5 = MP \times (1 - 0.70) \times (1 - 0.75) \)
\( 430.5 = MP \times 0.30 \times 0.25 \)
\( 430.5 = MP \times 0.075 \)
Solve for Marked Price (MP):
\( MP = \frac{430.5}{0.075} \)
\( MP = 5740 \)
The Marked Price of the item is ₹5,740.
Calculating Cost Price Using Marked Price and Profit
If no discount were given, the Selling Price would be the Marked Price (₹5,740). This price would yield a profit of 40%.
The formula relating Selling Price (SP), Cost Price (CP), and Profit Percentage is:
\( SP = CP \times (1 + profit\%) \)
Here, the Selling Price (without discount) is the Marked Price:
- \(SP = MP = ₹5740\)
- Profit Percentage = 40% or 0.40
Substitute these values:
\( 5740 = CP \times (1 + 0.40) \)
\( 5740 = CP \times 1.40 \)
Solve for Cost Price (CP):
\( CP = \frac{5740}{1.40} \)
\( CP = 4100 \)
Final Answer
The Cost Price of the item is ₹4,100.
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