A retailer marks a laptop 70% above its cost price. He offers a first discount of 20% on the marked price. During a sale, an additional discount of 15% is applied on the already discounted price. If the final selling price is ₹39,312, what is the approximate cost price of the laptop?

The correct option is ₹34,000.

Step-by-step Explanation:

Step 1: Define the variables.
Let the Cost Price of the laptop be represented as $CP$.

Step 2: Calculate the Marked Price (MP).
The retailer marks the laptop 70% above its cost price.
Therefore, the Marked Price ($MP$) is given by:

$MP=CP+(0.70\times CP)=1.70\times CP$

Step 3: Calculate the price after the first discount.
A discount of 20% is applied on the marked price.
Price after the 1st discount =

$MP\times (1-0.20)=0.80\times MP$

Substituting $MP=1.70\times CP$ into the equation:

$\text{Price after 1st discount}=0.80\times 1.70\times CP=1.36\times CP$

Step 4: Calculate the final selling price after the second discount.
During the sale, an additional discount of 15% is applied on the already discounted price.
Final Selling Price ($SP$) =

$1.36\times CP\times (1-0.15)$

Simplifying this expression:

$SP=1.36\times CP\times 0.85=1.156\times CP$

Step 5: Equate to given Selling Price and solve for Cost Price ($CP$).
We are given that the final selling price is ₹39,312.

$1.156\times CP=39312$

Solving for $CP$:

$CP=\frac{39312}{1.156}\approx 34006.92$

Rounding off to the nearest given option, the approximate cost price of the laptop is ₹34,000.