A trader bought three kinds of nuts at #100 per kg, #84 pr kg and #60 per kg respectively and sold the mixed nuts to make a profit of 25% At what price per kg did he sell them?
Let's assume the trader bought x kg of nuts at #100 per kg, y kg of nuts at #84 per kg, and z kg of nuts at #60 per kg.
The total cost of buying these nuts would be:
100x + 84y + 60z
To make a 25% profit, the trader needs to sell the nuts at 125% of the cost price. This can be written as:
1.25(100x + 84y + 60z)
Simplifying this expression, we get:
125x + 105y + 75z
The trader sold a mixture of nuts, so the total quantity sold would be x + y + z kg.
Therefore, the selling price per kg would be:
(125x + 105y + 75z) / (x + y + z)
We don't have enough information to calculate x, y, and z, so we can't find the exact selling price per kg. However, we can simplify the expression using the fact that x + y + z = total quantity of nuts sold.
Let's say the total quantity sold was N kg. Then we have:
x + y + z = N
Solving for one of the variables, say z, we get:
z = N - x - y
Substituting this into the expression for the selling price per kg, we get:
(125x + 105y + 75(N - x - y)) / N
Simplifying this expression, we get:
(50x + 30y + 75N) / N
This is the selling price per kg as a function of x, y, and N. We still don't know x and y, but we can find the minimum and maximum possible values for this expression.
The minimum value would occur if the trader bought only #60 per kg nuts. In that case, x = 0 and y = 0, so we have:
(50x + 30y + 75N) / N = 75
The maximum value would occur if the trader bought only #100 per kg nuts. In that case, y = 0 and z = 0, so we have:
(125x + 75N) / N = 125 - 50/N
So the selling price per kg would be between 75 and 125 - 50/N. Without knowing the exact values of x, y, and N, we can't give a more precise answer.
To find out at what price per kg the trader sold the mixed nuts, we need to calculate the average cost price and then add 25% profit.
Step 1: Calculate the total cost price of all the nuts.
The trader bought three kinds of nuts at different prices per kg.
Cost of the first kind of nuts = #100 per kg
Cost of the second kind of nuts = #84 per kg
Cost of the third kind of nuts = #60 per kg
Step 2: Calculate the weights of each kind of nuts.
Let's assume the weights of the three kinds of nuts are x, y, and z kg respectively.
Step 3: Calculate the total cost of each kind of nuts.
Total cost of the first kind of nuts = #100 * x
Total cost of the second kind of nuts = #84 * y
Total cost of the third kind of nuts = #60 * z
Step 4: Calculate the total cost of all the nuts.
Total cost = Total cost of the first kind + Total cost of the second kind + Total cost of the third kind
Total cost = (#100 * x) + (#84 * y) + (#60 * z)
Step 5: Calculate the average cost price per kg.
Average cost price = Total cost / Total weight
Average cost price = (Total cost of all nuts) / (x + y + z)
Step 6: Calculate the selling price with a 25% profit
Selling price = Average cost price + 25% of Average cost price
Let's assume x = 1kg, y = 2kg, z = 3kg to find the selling price per kg.
Plug in the values into the above formulas and calculate accordingly.
Total cost = (#100 * 1) + (#84 * 2) + (#60 * 3) = #100 + #168 + #180 = #448
Average cost price = #448 / (1 + 2 + 3) = #448 / 6 = #74.67 (rounded to 2 decimal places)
Profit = 25% of #74.67 = 0.25 * #74.67 = #18.67
Selling price = Average cost price + Profit = #74.67 + #18.67 = #93.34 (rounded to 2 decimal places)
Therefore, the trader sold the mixed nuts at #93.34 per kg.
To solve this problem, we can start by calculating the average price at which the trader bought the nuts. Then, we can determine the selling price per kg to make a profit of 25%.
Step 1: Calculate the average price per kg at which the trader bought the nuts.
The trader bought three kinds of nuts: one at #100 per kg, one at #84 per kg, and one at #60 per kg. To calculate the average price, we need to find the total cost of the nuts.
Cost of nuts #100 per kg = #100/kg
Cost of nuts #84 per kg = #84/kg
Cost of nuts #60 per kg = #60/kg
We need to calculate the total cost.
Total cost = Cost of nuts #100 per kg + Cost of nuts #84 per kg + Cost of nuts #60 per kg
Total cost = #100/kg + #84/kg + #60/kg
Now, we can add the costs together:
Total cost = #100 + #84 + #60
Total cost = #244
Step 2: Determine the selling price per kg to make a profit of 25%.
To calculate the selling price with a profit of 25%, we need to add 25% of the total cost to the total cost.
Profit = 25% of Total cost
Profit = 25/100 * #244
Profit = #61
Selling price per kg = Total cost + Profit
Selling price per kg = #244 + #61
Selling price per kg = #305
Therefore, the trader sold the mixed nuts at #305 per kg to make a profit of 25%.