Directions (74-78): Study the following information carefully and answer the questions given below.

Seven persons- A, B, C, D, E, F and G were born in different years – 1969, 1973, 1978, 1982, 1988, 1990 and 1995 but not necessarily in the same order. Age of each person is calculated on the base year 2022. C is two years elder than E. The age difference between F and E is a perfect cube number. The number of persons born after E is same as the number of persons born before D. The difference between the age of D and B is a prime number. A is older than G.

What is the sum of the ages of D, B and F?

Correct Answer: 133 years

Let's solve the puzzle step-by-step to find the ages of each person based on the given base year 2022.

Step 1: Calculate the age of each person for the given birth years (Base year: 2022):
- 1969: 2022 - 1969 = 53 years old
- 1973: 2022 - 1973 = 49 years old
- 1978: 2022 - 1978 = 44 years old
- 1982: 2022 - 1982 = 40 years old
- 1988: 2022 - 1988 = 34 years old
- 1990: 2022 - 1990 = 32 years old
- 1995: 2022 - 1995 = 27 years old

The ordered list of birth years (from oldest to youngest) and their ages is:
1. 1969 (53)
2. 1973 (49)
3. 1978 (44)
4. 1982 (40)
5. 1988 (34)
6. 1990 (32)
7. 1995 (27)

Step 2: Apply the given conditions:

1. "C is two years elder than E."
The difference between the ages of C and E must be 2 years (or E's birth year - C's birth year = 2 years).
Looking at the ages: 34 - 32 = 2 years.
So, C was born in 1988 (age 34) and E was born in 1990 (age 32).

2. "The number of persons born after E is same as the number of persons born before D."
E was born in 1990 (6th position in birth order). The number of persons born after E is 1 (born in 1995).
Therefore, the number of persons born before D must also be 1.
So, D was born in 1973 (2nd position in birth order), which means D's age is 49.

3. "The age difference between F and E is a perfect cube number."
E's age is 32. Perfect cubes are 1, 8, 27, 64, etc.
Let's check the age difference between E (32) and other available ages:
- |53 - 32| = 21 (Not a perfect cube)
- |49 - 32| = 17 (Not a perfect cube)
- |44 - 32| = 12 (Not a perfect cube)
- |40 - 32| = 8 (Which is 2³, a perfect cube!)
- |27 - 32| = 5 (Not a perfect cube)
Thus, F's age must be 40 (born in 1982).

4. "The difference between the age of D and B is a prime number."
D's age is 49.
Remaining available birth years / ages for B, A, G are: 1969 (53), 1978 (44), 1995 (27).
Let's test these ages with D (49):
- If B is 53: |49 - 53| = 4 (Not prime)
- If B is 44: |49 - 44| = 5 (5 is a prime number!)
- If B is 27: |49 - 27| = 22 (Not prime)
Therefore, B was born in 1978 (age 44).

5. "A is older than G."
The remaining ages are 53 and 27.
Since A is older than G, A must be 53 (born in 1969) and G must be 27 (born in 1995).

Step 3: Final arrangement of persons with their ages:
- A = 53 years
- D = 49 years
- B = 44 years
- F = 40 years
- C = 34 years
- E = 32 years
- G = 27 years

Step 4: Calculate the sum of the ages of D, B, and F:

$\text{Sum}=\text{Age of D}+\text{Age of B}+\text{Age of F}$

$\text{Sum}=49+44+40=133\text{years}$

Thus, the required sum of the ages of D, B, and F is 133 years.