A sold two items, X and Y, at 25% and 35% profit, respectively. If the difference between their profit is Rs 750 and the cost price of both items is the same, find the cost price of item X.

To find the cost price of item X, let us break down the problem step-by-step:

Step 1: Define the variables
Let the cost price (CP) of both items X and Y be
$CP$
since the question states that the cost price of both items is the same.

Step 2: Calculate the profit for each item
Profit on item X is 25% of its cost price:
$\text{Profit on X}=25\%\text{of}CP=0.25\times CP$
Profit on item Y is 35% of its cost price:
$\text{Profit on Y}=35\%\text{of}CP=0.35\times CP$

Step 3: Set up the equation using the difference in profit
The difference between the profits of the two items is given as Rs 750. Therefore:
$\text{Profit on Y}-\text{Profit on X}=750$
Substituting the expressions we found:
$0.35CP-0.25CP=750$
$0.10CP=750$

Step 4: Solve for the cost price (CP)
Divide both sides of the equation by 0.10 to find the cost price:
$CP=\frac{750}{0.10}$
$CP=7500$

Thus, the cost price of item X is Rs 7500.