Let's break down the information given:

• Rahim paid for 1 part of the total amount.
• Karim paid TK 17, which we can consider as x parts of the total amount.
• James paid the rest, which means he paid the remaining parts of the total amount after Rahim and Karim paid their portions.

Since Rahim paid for 1 part and Karim paid for x parts, the total parts paid by Rahim and Karim together is 1 + x.

And we know that James paid the rest, which means he paid the remaining parts, which can be calculated as the total parts (1 + x) minus the parts paid by Rahim and Karim.

So, James paid (Total parts - Parts paid by Rahim and Karim) = (1 + x) - 1 = x parts.

Now, we know that Karim paid TK 17, which is x parts of the total amount. So, 17 is x parts.

We can set up a proportion to find out the value of 1 part:

This is because the total amount paid is TK 45, and there are 3 people in total. Each part corresponds to TK 45/3.

Now, let's solve for x:

Cross multiply:

Divide both sides by 45:

Now, let's find out how much James paid, which is x parts:

To simplify this fraction:

So, James paid 17/15 parts of the total amount.

Now, to find out what fraction of the total amount James paid, we can express this as a fraction:

To simplify this, we can multiply the numerator and denominator by 15:

So, James paid 17/45 fraction of the total amount.

Looking at the options, none of them exactly match with 17/45. But, we can simplify the fraction to find the closest match.