By selling a TV to Opio at sh 275,000, Odongo made a profit of 10%. Opio sold the radio at a loss of 8% to Joseph. How much did Odongo pay for the radio?

Let's first calculate how much Odongo paid for the TV:

Let the cost price of the TV be x.

Since Odongo made a profit of 10%, the selling price of the TV is 110% of the cost price:
Selling price = 1.10x = 275,000

From this, we can calculate the cost price of the TV:
1.10x = 275,000
x = 275,000 / 1.10
x = 250,000

So, Odongo paid sh 250,000 for the TV.

Now, let's calculate how much Opio paid for the radio:

Opio sold the TV at a loss of 8%, so the selling price of the radio is 92% of the cost price:
Selling price = 0.92y = 250,000

From this, we can calculate the cost price of the radio:
0.92y = 250,000
y = 250,000 / 0.92
y ≈ 271,739.13

Therefore, Odongo paid approximately sh 271,739.13 for the radio.