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?

Correct Answer: The correct option is 37 years.

Step-by-step Explanation:

Step 1: Understanding the seating arrangement

There are 7 positions in a row (facing South). Let's number the positions from 1 to 7 from Left to Right.

Since all persons face South:

• "Right" means moving towards the left side (towards position 1).

• "Left" means moving towards the right side (towards position 7).

Step 2: Placing the persons in the row

1. "E sits 2nd from one of the extreme ends."

Case 1: E is at position 2.

Case 2: E is at position 6.

2. "Three persons sit between E and the one who is 25 years old."

In Case 1 (E at 2): The person who is 25 years old must sit at position 6.

In Case 2 (E at 6): The person who is 25 years old must sit at position 2.

3. "The one who is 25 years old is the only neighbour of A."

This means A must be sitting at an extreme end next to the 25-year-old person.

In Case 1: The 25-year-old is at position 6, so A must be at position 7 (extreme right end).

In Case 2: The 25-year-old is at position 2, so A must be at position 1 (extreme left end).

4. "C is 15 years old and sits 3rd to the right of E."

Facing South, 3rd to the right means 3 places towards position 1 (leftwards in terms of 1-7 layout).

In Case 1 (E at position 2): 3rd to the right would be outside the row (position -1). So Case 1 is eliminated.

In Case 2 (E at position 6): 3rd to the right of E is position 3. So C is at position 3, and Age of C = 15 years.

Let's summarize Case 2 arrangement so far:

Positions (1 to 7):

• Position 1: A

• Position 2: Person (Age = 25)

• Position 3: C (Age = 15)

• Position 4: ?

• Position 5: ?

• Position 6: E

• Position 7: ?

5. "G sits at one of the extreme ends."

Position 1 is occupied by A, so G must be at position 7 (extreme right end).

6. "F sits to the right of B."

The remaining positions for B, D, and F are 2, 4, and 5.

Since F is to the right of B (facing South, meaning F is towards position 1 relative to B), B cannot be at position 2 if F is to its right, but position 2 is vacant for B/D/F.

Wait, if position 2 is the 25-year-old person, let's see who is at position 2, 4, 5:

If B is at position 5, then F must be at position 4 or 2.

Let's check: "D sits to the right of C."

Since C is at position 3, the positions to the right of C are 2 and 1.

Position 1 is A, so D MUST be at position 2!

Therefore, D is at position 2, and D's age = 25 years.

Now, remaining positions 4 and 5 are for B and F.

Since F sits to the right of B (towards position 1), F must be at position 4 and B must be at position 5.

The complete seating order from position 1 to 7 is:

A (1), D (2), C (3), F (4), B (5), E (6), G (7)

Step 3: Calculating the Ages

1. "The Age of D is equal to the total age of his immediate neighbours."

Immediate neighbours of D (at position 2) are A (position 1) and C (position 3).

Age of D = Age of A + Age of C

25 = Age of A + 15

Age of A = 25 - 15 = 10 years.

2. "B is 10 years older than A."

Age of B = Age of A + 10 = 10 + 10 = 20 years.

3. "B is 10 years younger than G."

Age of G = Age of B + 10 = 20 + 10 = 30 years.

4. "B is 1 year younger than E."

Age of E = Age of B + 1 = 20 + 1 = 21 years.

5. "Age of E is thrice of age of F."

Age of E = 3 × (Age of F)

21 = 3 × (Age of F)

Age of F = 21 / 3 = 7 years.

Step 4: Finding the required sum

We need to find the sum of the ages of F and G:

Sum = Age of F + Age of G

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

Thus, the sum of the ages of F and G is 37 years.