A television set is sold for ₹Q and the shopkeeper earns a profit of 25%. During a clearance sale, he marks the same set at 1.4Q and allows a discount of 15% on the marked price. What is his profit percentage during the sale?

The correct option is 48.75%.

Step 1: Determine the Cost Price (CP) of the television set.

Let the cost price of the television set be $\mathrm{CP}$.

Initially, the television set is sold for $\mathrm{₹Q}$ at a profit of 25%.

Using the relationship between Selling Price ($\mathrm{SP}$), Cost Price ($\mathrm{CP}$), and Profit percentage:

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

Substitute $\mathrm{SP}=Q$ and Profit % = 25:

$Q=\mathrm{CP}\times \left(1+\frac{25}{100}\right)$

$Q=\mathrm{CP}\times 1.25$

Expressing $\mathrm{CP}$ in terms of $Q$:

$\mathrm{CP}=\frac{Q}{1.25}=0.8Q$

Step 2: Calculate the new Selling Price during the clearance sale.

During the sale, the Marked Price ($\mathrm{MP}$) is set to $1.4Q$ and a discount of 15% is offered on this marked price.

The formula for the new Selling Price (${\mathrm{SP}}_{\text{sale}}$) after discount is:

${\mathrm{SP}}_{\text{sale}}=\mathrm{MP}\times \left(1-\frac{\text{Discount \%}}{100}\right)$

Substitute $\mathrm{MP}=1.4Q$ and Discount % = 15:

${\mathrm{SP}}_{\text{sale}}=1.4Q\times \left(1-\frac{15}{100}\right)$

${\mathrm{SP}}_{\text{sale}}=1.4Q\times 0.85=1.19Q$

Step 3: Calculate the profit percentage during the clearance sale.

The profit amount during the clearance sale is:

$\text{Profit}={\mathrm{SP}}_{\text{sale}}-\mathrm{CP}$

$\text{Profit}=1.19Q-0.8Q=0.39Q$

Now, calculate the profit percentage relative to the original Cost Price ($\mathrm{CP}$):

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

$\text{Profit \%}=\left(\frac{0.39Q}{0.8Q}\right)\times 100$

$\text{Profit \%}=\frac{0.39}{0.8}\times 100=48.75\%$

Hence, the profit percentage earned during the clearance sale is 48.75%.