A store sold 3 items with selling prices in ratio 4:5:6. Profit/loss: 25% profit, 15% loss, 20% profit respectively. What is approximate total profit/loss percentage?

The correct answer is 6.5% profit.

Let's solve the problem step-by-step to calculate the total profit or loss percentage.

Step 1: Understand the given selling prices and ratios.
The selling prices (SP) of the three items are in the ratio $4:5:6$.
For simplicity in calculation, let us assume the selling prices of the three items are:
Selling Price of Item 1 (${\text{SP}}_1$) = 400
Selling Price of Item 2 (${\text{SP}}_2$) = 500
Selling Price of Item 3 (${\text{SP}}_3$) = 600

Total Selling Price (${\text{SP}}_{\text{total}}$) = 400 + 500 + 600 = 1500

Step 2: Calculate the Cost Price (CP) for each item.
The relationship between Selling Price (SP), Cost Price (CP), and profit/loss percentage is given by:

$\text{SP}=\text{CP}\times \left(1+\frac{\text{Profit \%}}{100}\right)$

or, for a loss:

$\text{SP}=\text{CP}\times \left(1-\frac{\text{Loss \%}}{100}\right)$

For Item 1: 25% profit
$400={\text{CP}}_1\times \left(1+\frac{25}{100}\right)={\text{CP}}_1\times 1.25$

${\text{CP}}_1=\frac{400}{1.25}=320$

For Item 2: 15% loss
$500={\text{CP}}_2\times \left(1-\frac{15}{100}\right)={\text{CP}}_2\times 0.85$

${\text{CP}}_2=\frac{500}{0.85}=\frac{10000}{17}\approx 588.235$

For Item 3: 20% profit
$600={\text{CP}}_3\times \left(1+\frac{20}{100}\right)={\text{CP}}_3\times 1.20$

${\text{CP}}_3=\frac{600}{1.20}=500$

Step 3: Calculate the total Cost Price (CP).
${\text{CP}}_{\text{total}}=320+588.235+500=1408.235$

Step 4: Determine overall Profit/Loss and its percentage.
Since ${\text{SP}}_{\text{total}}>{\text{CP}}_{\text{total}}$, there is an overall profit.

$\text{Total Profit}={\text{SP}}_{\text{total}}-{\text{CP}}_{\text{total}}=1500-1408.235=91.765$

$\text{Profit \%}=\left(\frac{\text{Total Profit}}{{\text{CP}}_{\text{total}}}\right)\times 100$

$\text{Profit \%}=\left(\frac{91.765}{1408.235}\right)\times 100\approx 6.516\%$

Hence, the approximate total profit percentage is 6.5% profit.