Directions (71-75) : Study the following information carefully and answer the question given below:

Seven persons sit in a row facing to the south and they all have different ages. E sits 2nd from one of the extreme ends. Three persons sit between E and the one who is 25 years old. The one who is 25 years old is the only neighbour of A. D sits to the right of C. The Age of D is equal to the total age of his immediate neighbours. C is 15 years old and sits 3 rd to the right of E. B is 10 years older than A and 10 years younger than G who sits at one of the extreme ends. F sits to the right of B who is 1 year younger than E whose age is thrice of age of F.

What is the sum of the ages of F and G?

`. Let's carefully construct the solution tags. 37 years

The correct answer is 37 years.

Step-by-step Explanation:

Let us determine the seating arrangement and ages of all seven persons sitting in a row facing South.
Since all persons face South, "Right" corresponds to moving towards the left end of the row (Positions 1 to 7 from Left to Right), and "Left" corresponds to moving towards the right end of the row.

Step 1: Determine the positions of E, C, A, and G
1. E sits 2nd from one of the extreme ends.
2. Three persons sit between E and the person who is 25 years old.
3. The 25-year-old person is the only neighbour of A, which means A must sit at an extreme end (Position 1 or Position 7).
4. G also sits at one of the extreme ends.
5. C is 15 years old and sits 3rd to the right of E (towards lower position numbers).

If E were at Position 2 from the left, 3rd to the right of E would fall outside the row. Therefore, E must be at Position 6 (2nd from the right end).

Using E at Position 6:
- 3rd to the right of E is Position 3, so C (15 years old) is at Position 3.
- Three persons sit between E (Pos 6) and the 25-year-old person, placing the 25-year-old at Position 2.
- Since Position 2 has only one neighbour at the extreme left, A is at Position 1.
- Since A is at Position 1, G must be at the other extreme end, Position 7.

Step 2: Determine the position and age of D and A
1. D sits to the right of C (towards lower position numbers). The only vacant position to the right of C is Position 2.
Thus, D is at Position 2 and D is 25 years old.

2. The age of D is equal to the total age of his immediate neighbours (A at Pos 1 and C at Pos 3):

$\text{Age of D}=\text{Age of A}+\text{Age of C}$

$25=\text{Age of A}+15$

$\text{Age of A}=10\text{years}$

Step 3: Determine the ages of B, G, E, and F
1. B is 10 years older than A:

$\text{Age of B}=10+10=20\text{years}$

2. B is 10 years younger than G:

$\text{Age of G}=20+10=30\text{years}$

3. B is 1 year younger than E:

$\text{Age of E}=20+1=21\text{years}$

4. The age of E is thrice the age of F:

$\text{Age of E}=3\times \text{Age of F}$

$21=3\times \text{Age of F}$

$\text{Age of F}=7\text{years}$

Step 4: Calculate the required sum
We need to find the sum of the ages of F and G:

$\text{Sum}=\text{Age of F}+\text{Age of G}$

$\text{Sum}=7+30=37\text{years}$