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 D, F and E?

The correct option is 53 years.

Step-by-Step Explanation:

Let us analyze the seating arrangement and calculate the ages of all individuals step-by-step.

1. Seating Arrangement:
There are 7 persons sitting in a row facing South.
Since they are facing South:
- Right is towards the Left direction on paper.
- Left is towards the Right direction on paper.
Let positions from left to right on paper be numbered 1 to 7.

Step 1.1: Position of E and 25-year-old person
"E sits 2nd from one of the extreme ends."
So, E can be at position 2 or position 6.
"Three persons sit between E and the one who is 25 years old."
- Case 1: If E is at position 2, the 25-year-old person is at position 6.
- Case 2: If E is at position 6, the 25-year-old person is at position 2.

Step 1.2: Position of A
"The one who is 25 years old is the only neighbour of A."
This means A must be sitting at an extreme end (position 1 or position 7), adjacent to the 25-year-old person.
- In Case 1 (25-year-old at pos 6): A must be at position 7.
- In Case 2 (25-year-old at pos 2): A must be at position 1.

Step 1.3: Position of C
"C is 15 years old and sits 3rd to the right of E."
Since everyone is facing South, "3rd to the right of E" means 3 positions to the left of E on paper.
- In Case 1: E is at position 2, so 3 positions to the left on paper (towards position 1) would be out of bounds, or 3rd to the right of E (South facing) corresponds to Position (2 - 3), which is invalid. Wait! Facing South means:
- Facing South: Right = Left-hand side of paper (position decreases). Left = Right-hand side of paper (position increases).
Let us double check: 3rd to the right of E facing South means Position of E minus 3.
Thus, E cannot be at position 2 because E - 3 < 1.
Therefore, E must be at position 6!
Then 3rd to the right of E (facing South) is position $6-3=3$.
So C is at position 3, and Age of C = 15 years.
Let's re-verify the line-up (positions 1 to 7 from Left to Right on paper):
- Pos 1: A
- Pos 2: 25 years old
- Pos 3: C (15 years old)
- Pos 6: E

Step 1.4: Position of G, B, F, and D
"G sits at one of the extreme ends."
Since A is at position 1, G must be at position 7.
Now the remaining positions to fill are 2, 4, 5.
"F sits to the right of B" (facing South, F is to the left of B on paper, i.e., position of F < position of B).
"D sits to the right of C" (facing South, D is at position < 3).
Since C is at position 3, the only position available to the right of C (facing South, i.e. pos 1 or 2) is position 2 (since pos 1 is A).
Therefore, D is at position 2, and D is 25 years old.
Now remaining positions for B and F are 4 and 5.
Since F is to the right of B (facing South, position of F < position of B):
- F is at position 4.
- B is at position 5.

Thus, the complete seating arrangement from Position 1 to 7 (Left to Right on paper) is:
1: A
2: D (25 years)
3: C (15 years)
4: F
5: B
6: E
7: G

2. Age Calculations:

Step 2.1: Ages of E and F
"B is 1 year younger than E whose age is thrice of age of F."
Let the age of F be $x$.
Then, Age of E = $3x$.
Age of B = $3x-1$.

Step 2.2: Ages of A and G
"B is 10 years older than A" $\Rightarrow$ Age of A = Age of B - 10 = $(3x-1)-10=3x-11$.
"B is 10 years younger than G" $\Rightarrow$ Age of G = Age of B + 10 = $(3x-1)+10=3x+9$.

Step 2.3: Finding the value of F's age ($x$)
"The Age of D is equal to the total age of his immediate neighbours."
Immediate neighbours of D (at position 2) are A (at position 1) and C (at position 3).
Given:
- Age of D = 25
- Age of C = 15
- Age of A = $3x-11$

Setting up the equation:
$\text{Age of D}=\text{Age of A}+\text{Age of C}$
$25=(3x-11)+15$
$25=3x+4$
$3x=21$
$x=7$

So, the age of F is 7 years.

Step 2.4: Finding the age of E
Age of E = $3x=3\times 7=21$ years.

3. Sum of the Ages of D, F, and E:
- Age of D = 25 years
- Age of F = 7 years
- Age of E = 21 years

$\text{Sum}=\text{Age of D}+\text{Age of F}+\text{Age of E}$
$\text{Sum}=25+7+21=53\text{years}$

Hence, the sum of the ages of D, F, and E is 53 years.