Explanation:

Contract of Sale:
A contract of sale is a contract in which one party agrees to transfer the ownership of goods to another party in exchange for money. In this case, A is agreeing to deliver 100 kg of sugar to B, but there is no mention of any monetary consideration or payment involved. Therefore, it cannot be considered a contract of sale.

Agreement to Sell:
An agreement to sell is a contract in which one party agrees to transfer the ownership of goods to another party at a future date or upon the occurrence of a certain event. In this case, A is agreeing to deliver 100 kg of sugar to B, but there is no mention of a future date or any specific event upon which the transfer of ownership will occur. Therefore, it cannot be considered an agreement to sell.

Sale on Approval:
A sale on approval is a type of sale where the buyer has the option to approve or disapprove the goods after taking possession of them. In this case, there is no mention of B having the option to approve or disapprove the sugar after delivery. Therefore, it cannot be considered a sale on approval.

Barter:
Barter is a system of exchange where goods or services are directly exchanged for other goods or services without the use of money. In this case, A agrees to deliver 100 kg of sugar to B in exchange for 15 meters of cloth. This exchange of goods without the involvement of money is an example of barter. Therefore, the correct answer is option D - barter.

In conclusion, the agreement between A and B can be categorized as a barter agreement since it involves the exchange of goods (sugar and cloth) without the involvement of money.