An online retailer sets the regular selling price of an electronic device at ₹W, which yields a profit margin of 20%. When a promotional event is held, the item's tagged price is adjusted to ₹1.5W, and a promotional discount of 15% is applied to this tagged price. What is the profit percentage earned by the retailer during the promotional event?

The correct answer is 53%.

Here is the complete step-by-step derivation to calculate the profit percentage earned by the retailer during the promotional event:

Step 1: Determine the original Cost Price (CP)
Let the Cost Price of the item be CP.
The regular selling price is ₹W, which yields a profit margin of 20%.
This implies that the regular selling price is equal to 120% of the cost price:

$W=1.20\times \text{CP}$

Expressing CP in terms of W gives:

$\text{CP}=\frac{W}{1.20}$

Step 2: Calculate the promotional Selling Price
During the promotional event, the item's tagged price is set to ₹1.5W.
A promotional discount of 15% is applied to this tagged price.
Therefore, the promotional selling price (SP_promotional) is equal to 85% of the tagged price:

${\text{SP}}_{\text{promotional}}=1.5W\times (1-0.15)$

${\text{SP}}_{\text{promotional}}=1.5W\times 0.85=1.275W$

Step 3: Calculate the promotional profit percentage
The profit percentage during the promotional event is given by the standard formula:

$\text{Profit Percentage}=\left(\frac{{\text{SP}}_{\text{promotional}}-\text{CP}}{\text{CP}}\right)\times 100$

We can rewrite this expression as:

$\text{Profit Percentage}=(\frac{{\text{SP}}_{\text{promotional}}}{\text{CP}}-1)\times 100$

Now, evaluate the ratio of SP_promotional to CP using our expressions in terms of W:

$\frac{{\text{SP}}_{\text{promotional}}}{\text{CP}}=\frac{1.275W}{W/1.20}=1.275\times 1.20=1.53$

Substitute this value back into the profit percentage equation:

$\text{Profit Percentage}=(1.53-1)\times 100=0.53\times 100=53\%$

Thus, the profit percentage earned by the retailer during the promotional event is 53%.