A shopkeeper acquired two distinct items, X and Y, for identical prices. Subsequently, he traded item X at a profit of 20% and item Y at a loss of 10%. If his total net gain from the entire transaction amounted to Rs. 40, determine the purchase price of each item.

The correct option is Rs. 400.

Let's solve the problem step-by-step to find the purchase price (Cost Price) of each item.

Step 1: Understand the given information
Let the cost price (CP) of item X be $x$ rupees.
Since the shopkeeper acquired both items X and Y for identical prices, the cost price of item Y is also $x$ rupees.

$\text{Cost Price of X}=x$

$\text{Cost Price of Y}=x$

$\text{Total Cost Price of both items}=x+x=2x$

Step 2: Express profit and loss in terms of CP
Item X is sold at a profit of 20%:
$\text{Profit on item X}=20\%\text{of}x=\frac{20}{100}\times <!--\; \times \; -->x=0.20x$

Item Y is sold at a loss of 10%:
$\text{Loss on item Y}=10\%\text{of}x=\frac{10}{100}\times <!--\; \times \; -->x=0.10x$

Step 3: Calculate total net gain
The net gain from the entire transaction is equal to the profit earned on item X minus the loss incurred on item Y:
$\text{Net Gain}=\text{Profit on X}-\text{Loss on Y}$

$\text{Net Gain}=0.20x-0.10x=0.10x$

Step 4: Solve for the cost price ($x$)
We are given that the total net gain is Rs. 40. Therefore:
$0.10x=40$

$x=\frac{40}{0.10}=400$

Thus, the purchase price (Cost Price) of each item is Rs. 400.