20 chairs are sold for $400 each. If 10 of them are sold at a profit percentage of 60% and 10 of them are sold at a loss percentage of 20%, after selling all the chairs, what is th... 20 chairs are sold for $400 each. If 10 of them are sold at a profit percentage of 60% and 10 of them are sold at a loss percentage of 20%, after selling all the chairs, what is the overall profit or loss percentage? Read more

Steps to Solve

1. Calculate the total selling price of all chairs

The total selling price of all 20 chairs is given as $400 \times 20$.

$$ \text{Total Selling Price} = 400 \times 20 = 8000 $$

2. Find the cost price of chairs sold at a profit

For the 10 chairs sold at a profit of 60%, let the cost price be $C$. The selling price is:

$$ \text{Selling Price} = C + 0.6C = 1.6C $$

Since they are sold for $400 each:

$$ 10 \times 400 = 1.6C \implies 4000 = 1.6C \implies C = \frac{4000}{1.6} = 2500 $$

3. Find the cost price of chairs sold at a loss

For the 10 chairs sold at a loss of 20%, let the cost price be $C'$. The selling price is:

$$ \text{Selling Price} = C' - 0.2C' = 0.8C' $$

Again, they are sold for $400 each:

$$ 10 \times 400 = 0.8C' \implies 4000 = 0.8C' \implies C' = \frac{4000}{0.8} = 5000 $$

4. Calculate the total cost price of all chairs

The total cost price is the sum of the cost price of both sets of chairs:

$$ \text{Total Cost Price} = 2500 + 5000 = 7500 $$

5. Calculate the overall profit or loss

Now, find the overall profit:

$$ \text{Profit} = \text{Total Selling Price} - \text{Total Cost Price} = 8000 - 7500 = 500 $$

6. Calculate the overall profit percentage

To find the profit percentage:

$$ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Total Cost Price}} \right) \times 100 = \left( \frac{500}{7500} \right) \times 100 = \frac{50000}{7500} = 6.67% $$