A dealer buys an article listed at ₹250 and gets successive discounts of 12% and 16%. He spends 10% of the cost price on transportation. At what price should he sell the article to earn a profit of 25%? (Correct to two places of decimal)
Calculating Selling Price with Successive Discounts and Profit
This problem asks us to determine the selling price required to achieve a specific profit percentage after accounting for initial discounts and additional costs. We need to carefully calculate the cost price first.
1. Determining the Price After Successive Discounts
The dealer buys an article listed at a certain price and receives two sequential discounts. This means the second discount is applied to the price that remains after the first discount.
- Listed Price = ₹250
- First Discount = 12%
- Second Discount = 16%
To find the price after the first discount:
Price after 1st Discount = Listed Price $\times$ (1 - First Discount Rate)
Price after 1st Discount = ₹250 $\times$ (1 - $\frac{12}{100}$)
Price after 1st Discount = ₹250 $\times$ (1 - 0.12)
Price after 1st Discount = ₹250 $\times$ 0.88 = ₹220
Next, we apply the second discount to the ₹220 price:
Price after 2nd Discount = Price after 1st Discount $\times$ (1 - Second Discount Rate)
Price after 2nd Discount = ₹220 $\times$ (1 - $\frac{16}{100}$)
Price after 2nd Discount = ₹220 $\times$ (1 - 0.16)
Price after 2nd Discount = ₹220 $\times$ 0.84 = ₹184.80
So, the dealer acquires the article for ₹184.80 after the discounts.
2. Calculating the Total Cost Price (CP)
The dealer incurs additional expenses on transportation, which adds to the cost price.
- Price after discounts = ₹184.80
- Transportation Cost = 10% of the price after discounts
Calculate the transportation cost:
Transportation Cost = $\frac{10}{100} \times$ ₹184.80
Transportation Cost = 0.10 $\times$ ₹184.80 = ₹18.48
Now, add the transportation cost to find the total cost price (CP):
Total Cost Price (CP) = Price after discounts + Transportation Cost
Total Cost Price (CP) = ₹184.80 + ₹18.48 = ₹203.28
3. Determining the Selling Price (SP) for a 25% Profit
The goal is to sell the article at a price that yields a 25% profit over the total cost price.
- Total Cost Price (CP) = ₹203.28
- Desired Profit = 25%
The formula for calculating the selling price (SP) to achieve a desired profit is:
SP = CP $\times$ (1 + Profit Percentage)
SP = ₹203.28 $\times$ (1 + $\frac{25}{100}$)
SP = ₹203.28 $\times$ (1 + 0.25)
SP = ₹203.28 $\times$ 1.25 = ₹254.10
Therefore, the dealer should sell the article for ₹254.10 to achieve a 25% profit.
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