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.

The given birth years are 1998, 2000, 2003, 2004, 2005, 2010, 2012, 2015, and 2017.
Subtracting each birth year from 2021 gives their respective ages:

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

List of calculated ages: 23, 21, 18, 17, 16, 11, 9, 6, 4.

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

We are given that the ages of F, G, and I are all perfect squares.
Looking at our set of ages {23, 21, 18, 17, 16, 11, 9, 6, 4}, the perfect square ages are 16, 9, and 4.
Since I is the youngest and F is the oldest of the three:

• F = 16 years old (born in 2005)
• G = 9 years old (born in 2012)
• I = 4 years old (born in 2017)

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.
The remaining available ages are {23, 21, 18, 17, 11, 6}.
The pair from the remaining ages that adds up to 35 is 21 and 14, but 14 is not in our set. Checking other combinations:
23 + 12 = 35 (not available)
18 + 17 = 35 (both are available in our set!)

Since C is older than D:
• C = 18 years old (born in 2003)
• D = 17 years old (born in 2004)

Step 4: Determine the ages of A and B.

Remaining available ages: {23, 21, 11, 6}.
We are given that B is two years younger than A (Age of A - Age of B = 2).
From the remaining ages, 23 - 21 = 2.
Thus:

• A = 23 years old (born in 1998)
• B = 21 years old (born in 2000)

Step 5: Determine the ages of E and H.

Remaining available ages: {11, 6}.
We are given that E is older than H.
Therefore:

• E = 11 years old (born in 2010)
• H = 6 years old (born in 2015)

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

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

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

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