Some articles were marked $25\%$ above their cost price. One of such articles was sold at $20\%$ profit on the marked price and the other one was sold at $10\%$ loss on the marked price. Find the overall percentage profit.

1. Let the cost price ($\text{CP}$) of each article be $\text{Rs. }100$.
$$\text{Total CP of 2 articles}=100+100=\text{Rs. }200$$

$$\text{Marked Price (MP) of each article}=100\times 1.25=\text{Rs. }125$$

2. Calculate the selling price ($\text{SP}$) of the first article (sold at $20\%$ profit on $\text{MP}$):

$${\text{SP}}_1=125\times \left(1+\frac{20}{100}\right)=125\times 1.20=\text{Rs. }150$$

3. Calculate the selling price ($\text{SP}$) of the second article (sold at $10\%$ loss on $\text{MP}$):

$${\text{SP}}_2=125\times \left(1-\frac{10}{100}\right)=125\times 0.90=\text{Rs. }112.5$$

4. Find total selling price and overall profit:

$$\text{Total SP}=150+112.5=\text{Rs. }262.5$$

$$\text{Total Profit}=\text{Total SP}-\text{Total CP}=262.5-200=\text{Rs. }62.5$$

$$\text{Overall Profit Percentage}=\left(\frac{62.5}{200}\right)\times 100\%=31.25\%$$