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?

Answer 1

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.