Explanation:

The eligibility criteria for the Prime Minister of India are primarily linked to membership in Parliament. - **Option A (30 years):** This is the minimum age required to be a member of the Rajya Sabha (Council of States). While a Prime Minister can be a member of the Rajya Sabha, this is not the *absolute minimum* age for the post itself, as a Lok Sabha member can also become PM. - **Option B (25 years):** This is the correct answer. To become the Prime Minister of India, a person must be a member of either the Lok Sabha or the Rajya Sabha. The minimum age requirement to be a member of the Lok Sabha (House of the People) is $25$ years. Therefore, if an individual is elected to the Lok Sabha at the age of $25$, they are constitutionally eligible to be appointed as Prime Minister. This represents the lowest possible age for eligibility. - **Option C (40 years):** There is no constitutional provision or established convention that sets the minimum age for the Prime Minister at $40$ years. This option is factually incorrect. - **Option D (35 years):** This is the minimum age required to be eligible for election as the President or Vice President of India. It is not the minimum age for the Prime Minister.