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?

Correct Answer: 53 years

Step-by-step Explanation:

Let's deduce the seating arrangement and ages step-by-step from the given conditions.

1. Seating Position Analysis:

There are 7 persons sitting in a single row facing South. Let the 7 positions from Left to Right be 1, 2, 3, 4, 5, 6, 7.

Since everyone faces South, "Right" means moving towards the Left in visual representation (towards position 1), and "Left" means moving towards the Right (towards position 7).

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

This gives two possible cases for E's position:

Case 1: E is at position 2.

Case 2: E is at position 6.

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

In Case 1 (E at 2): The person aged 25 must be at position 2 + 3 + 1 = 6.

In Case 2 (E at 6): The person aged 25 must be at position 6 - 3 - 1 = 2.

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

A person can have only one neighbor if and only if they are sitting at an extreme end (position 1 or 7).

In Case 1: The person at 6 is 25 years old, so A must be at the extreme end position 7.

In Case 2: The person at 2 is 25 years old, so A must be at the extreme end position 1.

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

Since they face South, 3rd to the right of E means 3 places towards the left end (subtracting 3 from E's position number).

In Case 1 (E at position 2): 3rd to the right of E would be position 2 - 3 = -1 (not possible).

Therefore, Case 1 is eliminated.

In Case 2 (E at position 6): C sits at position 6 - 3 = 3.

So, C (15 years old) is at position 3.

Let's update the seating positions in Case 2:

Position 1: A

Position 2: 25 years old

Position 3: C (15 years old)

Position 4: ?

Position 5: ?

Position 6: E

Position 7: ?

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

Since position 1 is occupied by A, G must sit at the other extreme end, which is position 7.

Now, position 2 must be occupied by one of the remaining persons (B, D, or F).

Step 6: "F sits to the right of B" and "D sits to the right of C."

Since facing South, "to the right" means towards smaller position numbers (towards position 1).

Positions to the right of C (position 3) are position 1 (A) and position 2. Thus, D must sit at position 2.

Since the person at position 2 is 25 years old, Age of D = 25 years.

Now the positions are:

Position 1: A

Position 2: D (25 years old)

Position 3: C (15 years old)

Position 4: ?

Position 5: ?

Position 6: E

Position 7: G

The remaining positions to fill are 4 and 5 for B and F.

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

Thus, the complete seating arrangement from Position 1 to 7 is:

1: A | 2: D | 3: C | 4: F | 5: B | 6: E | 7: G

2. Age Calculations:

Let's determine the ages of all persons using the given relations:

1. Age of C = 15 years.

2. Age of D = 25 years.

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

The immediate neighbours of D are A (position 1) and C (position 3).

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

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

$\text{Age of A}=25-15=10\text{years}$

4. "B is 10 years older than A":

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

5. "B is 1 year younger than E":

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

6. "whose age (E's age) is thrice of age of F":

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

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

$\text{Age of F}=\frac{21}{3}=7\text{years}$

3. Sum of Ages of D, F, and E:

$\text{Sum}=\text{Age of D}+\text{Age of F}+\text{Age of E}$

$\text{Sum}=25+7+21=53\text{years}$

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