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. Who among the following was born in 2010?

The correct answer is None of the above (the person born in 2010 is G).

Let's step through the logical reasoning step-by-step to find the birth years of all nine individuals: A, B, C, D, E, F, G, H, and I.

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: Age = 2021 - 1998 = 23 years

• Born in 2000: Age = 2021 - 2000 = 21 years

• Born in 2003: Age = 2021 - 2003 = 18 years

• Born in 2004: Age = 2021 - 2004 = 17 years

• Born in 2005: Age = 2021 - 2005 = 16 years

• Born in 2010: Age = 2021 - 2010 = 11 years

• Born in 2012: Age = 2021 - 2012 = 9 years

• Born in 2015: Age = 2021 - 2015 = 6 years

• Born in 2017: Age = 2021 - 2017 = 4 years

The set of available ages is: {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 list of ages {23, 21, 18, 17, 16, 11, 9, 6, 4}, the perfect square numbers are 16, 9, and 4.

We are told that I is the youngest of the three and F is the oldest of the three. Therefore:

• Age of F = 16 (Born in 2005)

• Age of G = 11? No, 11 is not a square. The three square ages are 16, 9, and 4.

So, F = 16 (oldest), G = 9 (middle), and I = 4 (youngest).

• F's age = 16 → Born in 2005

• G's age = 9 → Born in 2012... Wait! Let's re-verify:

Wait, let's check the age of 11: 2021 - 2010 = 11. Is 11 a square? No, 16, 9, and 4 are squares. So F = 16 (born 2005), G = 9 (born 2012), I = 4 (born 2017).

Step 3: Determine the ages of C and D.

We are given that the sum of the ages of C and D is 35, and C is older than D.

The remaining available ages after removing 16, 9, and 4 are: {23, 21, 18, 17, 11, 6}.

Pairs from remaining ages that add up to 35:

$23+12$ (12 is not available)

$21+14$ (14 is not available)

$18+17=35$ (Both 18 and 17 are available!)

Since C is older than D:

• C's age = 18 → Born in 2003

• D's age = 17 → Born in 2004

Step 4: Determine the ages of A and B.

We are given that B is two years younger than A (Age of B = Age of A - 2).

The remaining ages available are: {23, 21, 11, 6}.

Looking at the remaining ages, the only pair with a difference of 2 years is 23 and 21 ($23-21=2$).

Since B is younger than A:

• A's age = 23 → Born in 1998

• B's age = 21 → Born in 2000

Step 5: Determine the ages of E and H.

The remaining unassigned ages are {11, 6}.

We are given that E is older than H.

• E's age = 11 → Born in 2010

• H's age = 6 → Born in 2015

Summary of Birth Years:

• 1998 (Age 23): A

• 2000 (Age 21): B

• 2003 (Age 18): C

• 2004 (Age 17): D

• 2005 (Age 16): F

• 2010 (Age 11): E

• 2012 (Age 9): G

• 2015 (Age 6): H

• 2017 (Age 4): I

The person born in 2010 is E. Since E is not among options A, D, B, or C, the correct choice is None of the above.