Study the given information carefully and answer the questions given below.

Nine people A, B, C, D, E, F, G, H, and I were born in different years i.e., 1998, 2000, 2003, 2004, 2005, 2010, 2012, 2015, and 2017 on the same date i.e., 31st December but not necessarily in the same order. Their ages are calculated as of 31st December 2021.

B is two years younger than A. The sum of the ages of C and D is 35, and C is older than D. The ages of F, G, and I are all perfect squares, where I is the youngest of the three and F is the oldest of the three. E is older than H. What will be the sum of the present ages of E and G?

The correct answer is 20 years.

Step 1: Calculate the age of each person as of 31st December 2021.

Subtract each birth year from 2021:

• 1998: 2021 - 1998 = 23 years old
• 2000: 2021 - 2000 = 21 years old
• 2003: 2021 - 2003 = 18 years old
• 2004: 2021 - 2004 = 17 years old
• 2005: 2021 - 2005 = 16 years old
• 2010: 2021 - 2010 = 11 years old
• 2012: 2021 - 2012 = 9 years old
• 2015: 2021 - 2015 = 6 years old
• 2017: 2021 - 2017 = 4 years old

The available ages are: 23, 21, 18, 17, 16, 11, 9, 6, 4.

Step 2: Determine the ages of F, G, and I.

The ages of F, G, and I are all perfect squares.
Looking at the list of ages (23, 21, 18, 17, 16, 11, 9, 6, 4), the perfect squares are 16, 9, and 4.
Since F is the oldest and I is the youngest among the three:
• F's age = 16 years (Born in 2005)
• G's age = 9 years (Born in 2012)
• I's age = 4 years (Born in 2017)

Remaining available ages: 23, 21, 18, 17, 11, 6.

Step 3: Determine the ages of C and D.

The sum of the ages of C and D is 35, and C is older than D.
From the remaining ages (23, 21, 18, 17, 11, 6), the pair that sums to 35 is 18 and 17:

$18+17=35$

Since C is older than D:
• C's age = 18 years (Born in 2003)
• D's age = 17 years (Born in 2004)

Remaining available ages: 23, 21, 11, 6.

Step 4: Determine the ages of A and B.

B is two years younger than A.
Looking at the remaining ages (23, 21, 11, 6), the pair with a difference of 2 years is 23 and 21:

$23-21=2$

• A's age = 23 years (Born in 1998)
• B's age = 21 years (Born in 2000)

Remaining available ages: 11, 6.

Step 5: Determine the ages of E and H.

E is older than H.
Therefore, between 11 and 6:
• E's age = 11 years (Born in 2010)
• H's age = 6 years (Born in 2015)

Step 6: Calculate the sum of the present ages of E and G.

• Age of E = 11 years
• Age of G = 9 years

$\text{Sum}=11+9=20\text{years}$

The sum of the present ages of E and G is 20 years.