How many chocolates did Rakesh purchase if he bought some at a rate of 10 for Rs 1.50 and an equal number at 20 paise each, and later sold them at a rate of 20 for Rs 4, resulting in a profit of Rs 10?
To solve this problem, we need to use the concept of cost price, selling price, and profit.
Let's start by finding the cost price of the chocolates Rakesh bought.
Firstly, Rakesh bought some chocolates at a rate of 10 for Rs 1.50. In other words, the cost of 10 chocolates is Rs 1.50.
To find the cost of 1 chocolate, we divide the total cost by the number of chocolates:
Cost of 1 chocolate = Rs 1.50 / 10 = Rs 0.15
Similarly, Rakesh bought an equal number of chocolates at 20 paise each, which means the cost of 10 chocolates is 20 paise.
To find the cost of 1 chocolate, we convert paise to rupees and divide the total cost by the number of chocolates:
Cost of 1 chocolate = 20 paise / 100 = Rs 0.20 / 10 = Rs 0.02
So, Rakesh's total cost price for the chocolates he bought would be:
Cost price = (Cost of 10 chocolates at Rs 0.15 each) + (Cost of 10 chocolates at Rs 0.02 each)
Cost price = (10 * Rs 0.15) + (10 * Rs 0.02)
Cost price = Rs 1.50 + Rs 0.20
Cost price = Rs 1.70
Next, let's find the selling price of the chocolates.
Rakesh sold the chocolates at a rate of 20 for Rs 4. This means the selling price of 20 chocolates is Rs 4.
To find the selling price of 1 chocolate, we divide the total selling price by the number of chocolates:
Selling price of 1 chocolate = Rs 4 / 20 = Rs 0.20
Finally, let's calculate the profit.
Profit = Selling price - Cost price
Profit = Rs 0.20 - Rs 0.17
Profit = Rs 0.03
We are given that the profit is Rs 10, so we can set up the equation:
Rs 0.03 * Number of chocolates = Rs 10
Solving this equation, we get:
Number of chocolates = Rs 10 / Rs 0.03
Number of chocolates = 333.33
Since we can't have a fraction of a chocolate, we round the number down to the nearest whole number.
Therefore, Rakesh purchased 333 chocolates.