A producer supplies merchandise to a distributor at a discount of 20% off the list price, along with an additional 5% surcharge on that discounted price. Subsequently, the distributor sells the items for ₹3,150 above their purchase cost, achieving a gain of 25%. Calculate the original list price of the merchandise.

The correct answer is ₹15,000.

Let's break down the problem step-by-step to find the original list price of the merchandise.

Step 1: Express the purchase cost in terms of the list price

Let the original list price of the merchandise be $L$.

First, the producer gives a 20% discount on the list price:
$\text{Discounted Price}=L-0.20L=0.80L$

Next, an additional 5% surcharge is added on this discounted price:
$\text{Purchase Cost (C)}=0.80L+(0.05\times 0.80L)$
$\text{Purchase Cost (C)}=0.80L\times 1.05=0.84L$

Step 2: Find the distributor's purchase cost from the gain

The distributor sells the items for ₹3,150 above their purchase cost, which represents a gain of 25% on the purchase cost:
$\text{Gain}=25\%\text{of}C=0.25C$

Given that Gain = ₹3,150:
$0.25C=3150$
$C=\frac{3150}{0.25}=12600$

So, the purchase cost of the distributor is ₹12,600.

Step 3: Calculate the original list price

Now, substitute the value of $C$ into our first equation:
$0.84L=12600$
$L=\frac{12600}{0.84}=15000$

Thus, the original list price of the merchandise is ₹15,000.