A man sold a radio for rupees 1980 and gained 10%. The radio was bought for:

To find the cost price of the radio, we need to understand that the selling price given in the problem is inclusive of the 10% profit.

Step 1: Let's denote the cost price (the price at which the man bought the radio) as X.

Step 2: According to the problem, the selling price (the price at which the man sold the radio) is 10% more than the cost price. This can be written as X + 10% of X.

Step 3: We know that the selling price is 1980 rupees. So, we can set up the equation X + 10% of X = 1980.

Step 4: To make the calculation easier, we can express 10% as 0.10. The equation then becomes X + 0.10X = 1980.

Step 5: Combining like terms gives us 1.10X = 1980.

Step 6: Finally, to find X (the cost price), we divide both sides of the equation by 1.10. This gives us X = 1980 / 1.10.

Step 7: Calculating the above expression gives us X = 1800.

So, the man bought the radio for 1800 rupees.