A shopkeeper sold an item at 20% gain. Had he bought it ₹50 cheaper and sold it at the same price, he would have gained 25%. Find the cost price of the item (in ₹).

Let the original cost price of the item be CP and the original selling price be SP.
Given that the item is sold at a 20% gain:

SP=1.20CP
According to the second condition:
New Cost Price (CP
′
) = CP−50
The selling price remains the same (SP
′
=SP), and the new gain is 25%:

SP=1.25CP
′

1.20CP=1.25(CP−50)
1.20CP=1.25CP−62.5
1.25CP−1.20CP=62.5
0.05CP=62.5
CP=
0.05
62.5
​
=1250
Thus, the original cost price of the item is ₹1,250.