Preeti is the daughter of Rajesh and Amit is the son of Ankita. Rajesh is the only son of Rajan, and Ankita is the daughter-in-law of Rajan. How is Preeti related to Amit?

Introduction / Context:
This question describes a family around Rajan, his only son Rajesh and a daughter-in-law Ankita. Their children are Preeti and Amit. You must determine how Preeti is related to Amit. The puzzle tests whether you can recognise that when a man has only one son and one daughter-in-law, those two must be married to each other, and their children are siblings, not cousins.

Given Data / Assumptions:
- Preeti is the daughter of Rajesh. - Amit is the son of Ankita. - Rajesh is the only son of Rajan. - Ankita is the daughter-in-law of Rajan. - Standard one-marriage, one-family assumptions are used.

Concept / Approach:
If Rajesh is the only son of Rajan and Ankita is the daughter-in-law of Rajan, Ankita must be married to Rajesh, because that is the only way she can be a daughter-in-law when Rajan has only one son. Therefore, Preeti and Amit, being children of Rajesh and Ankita respectively, share the same parents. Children of the same parents are siblings. Since Preeti is the daughter and Amit is the son, Preeti is Amit's sister.

Step-by-Step Solution:
Step 1: Note that Rajesh is described as the only son of Rajan. There is no other son. Step 2: Ankita is the daughter-in-law of Rajan. A daughter-in-law of Rajan must be married to his son. Step 3: Because Rajesh is Rajan's only son, Ankita must be married to Rajesh. That is how she becomes Rajan's daughter-in-law. Step 4: Preeti is given as the daughter of Rajesh. Under the marriage we just established, she is Rajesh and Ankita's daughter. Step 5: Amit is given as the son of Ankita. Since Ankita is married to Rajesh, Amit is also a child of Rajesh. Therefore, Amit and Preeti share the same parents. Step 6: When two people share both parents, they are siblings. With Preeti female and Amit male, Preeti is Amit's sister.

Verification / Alternative check:
Draw the family tree: place Rajan at the top. Below him, put his only son Rajesh, and next to Rajesh place Ankita as his wife. Under Rajesh and Ankita, draw two children: Preeti (daughter) and Amit (son). In this picture, Preeti and Amit are clearly in the same generation and from the same parents, making them siblings. There is no room for them to be cousins or aunt–nephew because those would require different parents or different generations.

Why Other Options Are Wrong:
- Mother: Preeti is given as a daughter in the same generation as Amit, not as his parent. - Cousin: Cousins come from different parents who are siblings, but Preeti and Amit share the same parents. - Aunt: An aunt would be of an older generation, a sibling of a parent. Preeti is in Amit's generation. - Niece: A niece would be the daughter of a sibling or sibling-in-law, again implying a generational gap.

Common Pitfalls:
A common confusion is to read daughter-in-law of Rajan and imagine Ankita as married to some other son of Rajan, thus treating Preeti and Amit as cousins. However, the phrase only son of Rajan completely removes this ambiguity: Rajesh is the only candidate for Ankita's husband. Another mistake is not checking that both Preeti and Amit must share both parents once the marriage is fixed. Carefully identifying the spouse of the only son is the key step.

Final Answer:
Preeti is Amit's sister.