Discussion

Explanation:

The seat numbers on the dining table can be defined as below:

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From b - if C is seated on seat no.5, then the one who is a professor is on the seat no. 6.
From f, g and d - C is a Director and E sits second to the left of C. Also, there is one person between C and Grandmother of Gargi. Therefore, Grandmother can be at seat no. 3 i.e. E or at seat no. 7. 
The Grandmother is seated to the immediate left of D who is a actor. So, there are two cases possible here:
If Grand mother is at seat no. 3, then D is at seat no. 4(CASE I ) and
If the Grandmother is at seat no. 7, the D is at seat no. 1(CASE II)
From h - Father, who is a doctor is between Professor and Sister of Gargi.
In Case II where Grandmother is at seat no. 7, the two neighbours of Professor are C(Director) and Grandmother. So in this case Father(Doctor) can't be between professor and a sister. So Case II gets eliminated.
Therefore, Grandmother is at seat no. 3 i.e. E is a Grandmother and D is at seat no. 4. Also, Father is at seat no. 7 and sister of Gargi is at seat no. 1.
From c and g - G, an artist is a sister of Gargi and is at seat no. 1. F, who is a Business person is at seat no. 2. As there are on three females in Gargi's family i.e. Mother, Sister and Grandmother and as G is a sister and E is a Grandmother of Gargi, therefore F is a Mother of Gargi.
So D is an actor is a Brother of Gargi.
Therefore the arrangement will be:
Seat no. 1 - G/Artist/Sister
Seat no. 2 - F/Business Person/Mother
Seat no. 3 - E/Minister/Grand Mother
Seat no. 4 - D/Actor/Brother
Seat no. 5 - C/Director/Grandfather or Uncle
Seat no. 6 - A or B/Professor/Grandfather or Uncle
Seat no. 7 - A or B/ Doctor/ Father
Therefore,if C is a Uncle, then Professor is a Grandfather.
Hence, option (a)

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