A dealer allows his customers a discount of 25% and still gains 25%. If an article costs ₹1600 to the dealer, then its marked price (nearest to one rupee) is:
₹2667
Understanding Dealer Pricing: Marked Price Calculation
This problem requires calculating the Marked Price (MP) of an article. We are given the Cost Price (CP), the discount percentage offered to the customer, and the profit percentage the dealer makes.
Key Formulas
- Selling Price (SP) = Cost Price (CP) × (1 + Profit Percentage)
- Selling Price (SP) = Marked Price (MP) × (1 - Discount Percentage)
Step-by-Step Calculation
1. Calculate the Selling Price (SP):
The dealer gains 25% on the cost price of ₹1600.
Using the formula: $SP = CP \times (1 + \text{Profit\%})$
$SP = ₹1600 \times \left(1 + \frac{25}{100}\right)$
$SP = ₹1600 \times (1 + 0.25)$
$SP = ₹1600 \times 1.25$
$SP = ₹2000$
2. Calculate the Marked Price (MP):
The dealer allows a 25% discount on the Marked Price (MP) to achieve the Selling Price (SP) of ₹2000.
Using the formula: $SP = MP \times (1 - \text{Discount\%})$
$₹2000 = MP \times \left(1 - \frac{25}{100}\right)$
$₹2000 = MP \times (1 - 0.25)$
$₹2000 = MP \times 0.75$
$MP = \frac{₹2000}{0.75}$
$MP = \frac{₹2000}{\frac{3}{4}}$
$MP = ₹2000 \times \frac{4}{3}$
$MP = \frac{₹8000}{3}$
$MP \approx ₹2666.67$
3. Round to the Nearest Rupee:
The question asks for the marked price nearest to one rupee.
Rounding ₹2666.67 to the nearest rupee gives ₹2667.
Conclusion
The marked price of the article is approximately ₹2666.67, which rounds to ₹2667.
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