Directions: Read the following information carefully and answer the questions given below.

Six persons A, B, C, D, E and F sit around a circular table facing towards the centre, with equal distance between adjacent persons. Each of them is of a different age. The sum of the ages of the persons sitting opposite to each other is 40 years. None of them is less than 15 years old and greater than 25 years old.

E's age is 24 years. F sits opposite to the person who is 21 years old. B, who is the youngest person, sits immediately to the left of D. A sits second to the right of F. D is 4 years older than A.

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

Correct Answer: 37

Step-by-Step Explanation:

1. Understand the Given Information:

• Six persons (A, B, C, D, E, and F) sit around a circular table facing towards the centre.
• Each person is of a different age between 15 and 25 years old (inclusive).
• The sum of the ages of any two persons sitting opposite to each other is always 40 years.

2. Determine the Ages of E and F:

• We are given that E's age is 24 years.
Since the sum of ages of opposite persons is 40 years, the age of the person sitting opposite to E is:

$40-24=16$ years.

• We are given that F sits opposite to the person who is 21 years old.
Therefore, the age of F is:

$40-21=19$ years.

3. Determine the Ages of A and D:

• We know that D is 4 years older than A, which gives:

$\mathrm{Age\; of\; D}=\mathrm{Age\; of\; A}+4$

• From the analysis of the available age combinations satisfying all conditions, the age of A is 18 years.
Thus, the age of D is:

$18+4=22$ years.

4. Calculate the Sum of the Ages of A and F:

• Age of A = 18 years
• Age of F = 19 years

Now, adding their ages together:

$18+19=37$ years.

Hence, the sum of the ages of A and F is 37.