Step 1: Look at what is being asked.
Ask in each case whether exchange happens through price and trade or through hereditary social duty. We will work it out by sorting the choices one at a time.
Step 2: Working through the choices, part 1.
We want the one system that does not run on buying and selling at a price. Check how each choice works.
Step 3: Working through the choices, part 2.
A hundi moves credit between traders and a haat is a market place. Both depend on trade and price, so choices 1 and 2 are out.
Step 4: Working through the choices, part 3.
The Nakarattars did banking and trade as their business. That is also market behaviour, so choice 3 is out.
Step 5: Working through the choices, part 4.
Jajmani links service castes and land owning castes through inherited duties and fixed shares. No open price is set. This is the non-market pattern, so choice 4 is in.
Final Answer:
Only the jajmani system works through social ties and not through the market, so option 4 is the answer. \[ \boxed{\text{Option 4}} \]