Study the following information carefully and answer the question given below:

Seven persons were born in seven different years viz. 1982, 1987, 1990, 1992, 1996, 1998 and 2000. They were born on the same date in the same month. Their ages are calculated on the base year of 2022.

E is 10 years older than Y. The number of persons who were born between E and Y is same as the number of persons who were born after R. The Age difference between R and Y is same as the age difference between E and Q. The Age difference between Q and W is 3 years more than the age difference between T and G. Not more than two persons were born between T and G.

What is the sum of the ages of W and R?

The correct option is 65 years (Option 2).

Let's solve this step-by-step by calculating the ages of all individuals based on the base year of 2022.

Step 1: Calculate the age of each person for their respective birth year (Base year = 2022).

• Born in 1982: Age = 2022 - 1982 = 40 years

• Born in 1987: Age = 2022 - 1987 = 35 years

• Born in 1990: Age = 2022 - 1990 = 32 years

• Born in 1992: Age = 2022 - 1992 = 30 years

• Born in 1996: Age = 2022 - 1996 = 26 years

• Born in 1998: Age = 2022 - 1998 = 24 years

• Born in 2000: Age = 2022 - 2000 = 22 years

List of ages in descending order: 40, 35, 32, 30, 26, 24, 22.

Step 2: Determine the positions of E and Y.

We are given that E is 10 years older than Y.

Looking at the ages: 40, 35, 32, 30, 26, 24, 22.

The only pair of ages with a difference of 10 years is 35 and 25 (not present) or 32 and 22.

Thus, Age of E = 32 years (Born in 1990) and Age of Y = 22 years (Born in 2000).

The persons born between E (1990) and Y (2000) are those born in 1992, 1996, and 1998. So, there are 3 persons born between E and Y.

Step 3: Determine the position of R.

The number of persons born between E and Y is 3, which is the same as the number of persons born after R.

Since 3 persons were born after R, R must be the 4th person from the top (or 4th oldest).

The 4th oldest person is aged 30 years (Born in 1992). So, Age of R = 30 years.

Step 4: Determine the position of Q.

The age difference between R and Y is equal to the age difference between E and Q.

Age difference between R (30) and Y (22) = 30 - 22 = 8 years.

Therefore, age difference between E (32) and Q must also be 8 years.

Possibilities for Q's age: 32 + 8 = 40 or 32 - 8 = 24.

Looking at the available ages, 40 (1982) and 24 (1998) are both available.

If Q = 24 years, then the remaining ages for W, T, G would be 40, 35, 26.

Let's check Q = 40 years (Born in 1982):

The remaining available birth years for W, T, G are 1987 (35 years), 1996 (26 years), and 1998 (24 years).

Step 5: Place W, T, and G.

We are given: "The Age difference between Q and W is 3 years more than the age difference between T and G."

If Q = 40 years, and W is one of {35, 26, 24}:

• If W = 35: |Q - W| = 40 - 35 = 5. Then |T - G| = 5 - 3 = 2. The remaining ages for T and G are 26 and 24, which have an age difference of 2 (26 - 24 = 2). This works perfectly!

Number of persons between T (1996) and G (1998) is 0, which satisfies "Not more than two persons were born between T and G".

So, W = 35 years (Born in 1987).

Final Person-Age Mapping:

• 1982 (40 yrs): Q

• 1987 (35 yrs): W

• 1990 (32 yrs): E

• 1992 (30 yrs): R

• 1996 (26 yrs): T / G

• 1998 (24 yrs): G / T

• 2000 (22 yrs): Y

Step 6: Calculate the sum of the ages of W and R.

Age of W = 35 years

Age of R = 30 years

Sum = 35 + 30 = 65 years.