Sudhkin bought 6 dozen tables at the cost of ₹6200 per dozen. He spent ₹8000 on their polishing and ₹2200 on transportation. Calculate the selling price of 6 dozen tables at a gain... Sudhkin bought 6 dozen tables at the cost of ₹6200 per dozen. He spent ₹8000 on their polishing and ₹2200 on transportation. Calculate the selling price of 6 dozen tables at a gain of 12%. A shopkeeper purchased 60 kg of rice at ₹120 per kg and mixed it with 40 kg of rice costing ₹200 per kg. At what rate per kg must he sell this mixture to make a profit of 20%?
Understand the Problem
The question involves calculating the cost price and selling price of tables and rice, including profit calculations. The first part calculates the selling price of tables after considering the total costs, while the second part calculates the selling price per kg of rice needed to achieve a specific profit percentage.
Answer
The selling price per kg of rice must be $182.4$.
Answer for screen readers
The selling price per kg of rice must be $182.4$ to achieve a profit of $20%$.
Steps to Solve
-
Calculate the Cost Price of the Tables
First, we find the total cost of purchasing and transporting the tables.
The formula is:
$$ \text{CP of 6 dozen tables} = (6 \times 6200) + 8000 + 2200 $$
Calculating gives:
$$ \text{CP} = 37200 + 8000 + 2200 = 47400 $$ -
Calculate the Selling Price with Profit
Next, we need to find the selling price of the tables while considering a 12% profit.
Profit is calculated using the formula:
$$ \text{SP} = \text{CP} + \left( \text{gain%} \times \frac{\text{CP}}{100} \right) $$
Thus,
$$ \text{SP} = 47400 + \left( 12 \times \frac{47400}{100} \right) $$
This results in:
$$ \text{SP} = 47400 + 5688 = 53088 $$ -
Determine Selling Price Per Table
To find the selling price for each table, divide the total selling price by the number of tables.
The total number of tables is:
$$ \text{Total tables} = 72 $$
So,
$$ \text{SP per table} = \frac{53088}{72} = 738.67 $$ -
Calculate Total Cost Price of Rice Mixture
For the rice problem, calculate the cost price of each type.
For the first type,
$$ \text{CP for 60 kg} = 60 \times 320 = 7200 $$
For the second type,
$$ \text{CP for 40 kg} = 40 \times 200 = 8000 $$
Then, total cost price:
$$ \text{Total CP} = 7200 + 8000 = 15200 $$ -
Calculate Selling Price Required for Desired Profit
To achieve a profit of 20%, we calculate the selling price needed.
Using the previous calculations, the required SP is:
$$ \text{SP for 100 kg} = \text{CP} + \left( 20 \times \frac{\text{CP}}{100} \right) $$
Thus,
$$ \text{SP} = 15200 + \left( 20 \times \frac{15200}{100} \right) = 15200 + 3040 = 18240 $$ -
Determine Selling Price Per Kg of Rice
Finally, calculate the selling price per kg to achieve this profit.
$$ \text{SP per kg} = \frac{18240}{100} = 182.4 $$
The selling price per kg of rice must be $182.4$ to achieve a profit of $20%$.
More Information
Such calculations involving cost price, selling price, and profit percentages are common in business and economics. Understanding how to manipulate these formulas helps in various financial assessments.
Tips
- Confusing cost price with selling price.
- Not converting units properly when calculating prices per kg.
- Forgetting to convert percentages into decimal form when calculating profits.
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