A retailer priced a piece of electronic equipment 30% higher than its original cost. Subsequently, the retailer offered two successive discounts of 15% and 10% on that price, incurring a loss of ₹220. Determine the marked price of the equipment.

The correct answer is ₹52,000.

Step-by-step Explanation:

Step 1: Define the variables and relationships

Let the original cost price (CP) of the electronic equipment be $x$.

The retailer priced the equipment 30% higher than its original cost price to set the marked price (MP).

$\text{Marked Price (MP)}=x+0.30x=1.30x$

Step 2: Calculate the effective Selling Price (SP) after successive discounts

The retailer offers two successive discounts of 15% and 10% on the marked price.

After a 15% discount, the price becomes 85% of the marked price:

$\text{Price after 1st discount}=0.85\times \text{MP}$

After a further 10% discount, the final selling price becomes 90% of the price after the first discount:

$\text{Selling Price (SP)}=0.90\times (0.85\times \text{MP})=0.765\times \text{MP}$

Substitute $\text{MP}=1.30x$ into the equation:

$\text{Selling Price (SP)}=0.765\times 1.30x=0.9945x$

Step 3: Calculate the Loss and find the Cost Price ($x$)

Loss is given by the formula:

$\text{Loss}=\text{Cost Price (CP)}-\text{Selling Price (SP)}$

Given that the loss is ₹220:

$220=x-0.9945x$

$220=0.0055x$

Solving for $x$:

$x=\frac{220}{0.0055}=\mathrm{40,000}$

So, the original Cost Price (CP) is ₹40,000.

Step 4: Determine the Marked Price

Now, calculate the Marked Price (MP) using $\text{MP}=1.30x$:

$\text{Marked Price}=1.30\times \mathrm{40,000}=\text{₹52,000}$

Thus, the marked price of the equipment is ₹52,000.