Each pair of:
2. By selling a fan at Rs. 1810, a dealer makes a profit of Rs. 60.
i. Find the cost price of the fan.
ii. Find his gain percent.
iii. At what price must it be sold to get 2% profit?
Answer (2)
The cost price of the fan is Rs. 1750, the gain percent is approximately 3.43%, and the selling price required for a 2% profit is Rs. 1785.
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Calculate the cost price by subtracting the profit from the selling price: CP = 1810 − 60 = 1750 .
Determine the gain percent using the formula: G ain P erce n t = 1750 60 × 100 = 3.43% .
Compute the selling price for a 2% profit: S P 2% = 1750 × 1.02 = 1785 .
The cost price is Rs. 1750, the gain percent is 3.43%, and the selling price for 2% profit is Rs. 1785 .
Explanation
Understanding the Problem The problem provides the selling price of a fan and the profit made on the sale. We need to find the cost price, the gain percent, and the selling price required to achieve a 2% profit.
Calculating the Cost Price First, we calculate the cost price (CP) by subtracting the profit from the selling price (SP). Given that the selling price is Rs. 1810 and the profit is Rs. 60, we have: CP = SP − P ro f i t = 1810 − 60 = 1750 So, the cost price of the fan is Rs. 1750.
Calculating the Gain Percent Next, we calculate the gain percent using the formula: G ain P erce n t = C os t P r i ce P ro f i t × 100 Substituting the values, we get: G ain P erce n t = 1750 60 × 100 = 3.428571428571429 Rounding to two decimal places, the gain percent is approximately 3.43%.
Calculating the Selling Price for 2% Profit Finally, we calculate the selling price required to get a 2% profit. This is given by: S P 2% = CP + ( 2/100 ) × CP = CP × ( 1 + 0.02 ) = 1.02 × CP Substituting the cost price, we get: S P 2% = 1.02 × 1750 = 1785 Therefore, the selling price to get a 2% profit is Rs. 1785.
Final Answer Therefore: i. The cost price of the fan is Rs. 1750. ii. The gain percent is approximately 3.43%. iii. The selling price to get 2% profit is Rs. 1785.
Examples
Imagine you're running a small business buying and selling items. Understanding cost price, profit margins, and how to calculate desired profit percentages is crucial. For instance, if you buy handmade bracelets for a certain cost and want to make a specific profit, these calculations help you set the right selling price. This ensures your business remains profitable and sustainable. Similarly, retailers use these calculations to determine sale prices or offer discounts while still maintaining a profit.
