Rakesh bought some chocolates at 10 for rs 1.50 and an equal number at 20 paise each. he sold them at a rate of 20 for rs 4 and made profit of rs 10. how many chocolates did he purchase.?
Let's solve the problem step-by-step:
Step 1: Let's assume the number of chocolates Rakesh bought at 10 for Rs 1.50 as 'x'.
Step 2: The cost of 'x' chocolates at 10 for Rs 1.50 would be (1.50/10) * x = 0.15 * x.
Step 3: Rakesh also bought an equal number of chocolates at 20 paise each. So, the cost of these chocolates would be (0.20/1) * x = 0.20x.
Step 4: The total cost of all chocolates is the sum of the cost of chocolates bought at 10 for Rs 1.50 and at 20 paise each, which is 0.15x + 0.20x = 0.35x.
Step 5: Rakesh sold these chocolates at a rate of 20 for Rs 4, which is (4/20) * x = 0.20x.
Step 6: The profit made by Rakesh is Rs 10. So, the selling price of the chocolates is the cost price plus the profit, which is 0.35x + 10.
Step 7: According to the given problem, the selling price is equal to 0.20x. So, we can write the equation as 0.35x + 10 = 0.20x.
Step 8: Solving the equation, we get: 0.35x - 0.20x = 10, which simplifies to 0.15x = 10.
Step 9: Dividing both sides of the equation by 0.15: x = 10 / 0.15 = 66.67.
Step 10: Since we cannot have a fraction of a chocolate, we can round off the value of 'x' to the nearest whole number. Therefore, Rakesh purchased 67 chocolates.
So, Rakesh purchased 67 chocolates.
To solve this question, let's break it down step by step:
Step 1: Calculate the cost price of 10 chocolates bought at Rs 1.50 each.
10 chocolates at Rs 1.50 each = Rs 15 (1.50 * 10 = 15).
Step 2: Calculate the cost price of an equal number of chocolates bought at 20 paise each.
Let's assume the number of chocolates bought at 20 paise each is x.
Cost price of x chocolates at 20 paise each = x * (20/100) = (x/5) paise.
Converting it to rupees, the cost price of x chocolates = (x/5) * (1/100) = x/500.
Step 3: Calculate the selling price of the total number of chocolates sold at a rate of 20 for Rs 4.
Let's assume the total number of chocolates bought is y.
Selling price of y chocolates at 20 for Rs 4 = (y/20) * 4 = y/5.
Step 4: Calculate the profit made by Rakesh.
Profit = Selling price - Cost price.
Profit = (y/5) - (15 + (x/500)).
Profit = (y/5) - (3000 + x)/500.
Step 5: According to the given information, Rakesh made a profit of Rs 10.
Setting up the equation, we have:
(y/5) - (3000 + x)/500 = 10.
Step 6: Simplify the equation:
y/5 - (3000 + x)/500 = 10.
Multiply both sides by 500 to get rid of the denominator:
100y - (3000 + x) = 5000.
100y - 3000 - x = 5000.
Step 7: Rearrange the equation:
100y - x = 8000.
Step 8: To find the values of x and y, we need more information or equations. The given information in the question is not sufficient to determine the values.
Therefore, we cannot calculate the number of chocolates Rakesh purchased based on the given information.