Solving for Cost Price with Discounts and Profit
The question asks for the Cost Price (CP) of an item. We are given the Selling Price (SP) after two successive discounts and the profit percentage if no discount were applied.
Calculate Marked Price (MP)
The selling price (SP) is given as ₹689.7 after discounts of 75% and 34%. The formula relating SP, MP, and successive discounts (D1, D2) is:
\(SP = MP × (1 - D1) × (1 - D2)\)
Substituting the given values:
\(₹689.7 = MP × (1 - 0.75) × (1 - 0.34)\)
\(₹689.7 = MP × (0.25) × (0.66)\)
\(₹689.7 = MP × 0.165\)
Now, solve for MP:
\(MP = \frac{₹689.7}{0.165}\)
\(MP = ₹4180\)
Calculate Cost Price (CP)
If the shopkeeper had not given any discount, the selling price would be equal to the marked price (MP = ₹4180). In this scenario, he would have earned a profit of 76%.
The relationship between Selling Price (SP), Cost Price (CP), and Profit Percentage is:
\(SP_{no\_discount} = CP × (1 + Profit\%)\)
Using the MP as the SP without discount:
\(₹4180 = CP × (1 + 0.76)\)
\(₹4180 = CP × 1.76\)
Solve for CP:
\(CP = \frac{₹4180}{1.76}\)
\(CP = ₹2375\)
Conclusion
The Cost Price (CP) of the item is ₹2375.
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