A furniture showroom offers a sofa set at a 62% reduction from its listed price. Had the reduction been 52% instead, the selling price would be Rs. 8,000 higher. What is the listed price of the sofa set?

The correct option is Rs. 80,000.

To find the listed price of the sofa set, we can analyze the relationship between the discount percentages and the final selling prices.

Let the listed price of the sofa set be $L$ rupees.

Step 1: Determine the selling price for each reduction.

When an item is sold at a reduction (discount), the customer pays the remaining percentage of the original listed price.

At a 62% reduction, the selling price (${\text{SP}}_1$) is:

${\text{SP}}_1=(100-62)\%\text{of}L=38\%\text{of}L$

At a 52% reduction, the selling price (${\text{SP}}_2$) is:

${\text{SP}}_2=(100-52)\%\text{of}L=48\%\text{of}L$

Step 2: Set up the equation using the price difference.

We are given that a 52% reduction results in a selling price that is Rs. 8,000 higher than a 62% reduction. Therefore:

${\text{SP}}_2-{\text{SP}}_1=8000$

$48\%\text{of}L-38\%\text{of}L=8000$

$(48-38)\%\text{of}L=8000$

$10\%\text{of}L=8000$

Step 3: Calculate the total listed price ($L$).

Since 10% of the listed price equals Rs. 8,000, we convert 10% into fraction form and solve for $L$:

$\frac{10}{100}\times L=8000$

$L=8000\times 10$

$L=80000$

Hence, the listed price of the sofa set is Rs. 80,000.