Six individuals Tarun, Charu, Visakha, Monika, Anko, and Viraj were born in different years with the current base year as 2018. None of them is older than 90 years. Each person likes a different fruit: apple, orange, grapes, cherry, mango, and banana. The following conditions apply:

- The last two digits or the reverse of the last two digits of the birth year of a person can represent the age of another person. (For example, if A was born in 1943, then the age of B can be either 34 or 43.)
- Tarun was born in 1983.
- The age difference between Tarun and Charu is 21 years.
- Visakha's age is the sum of the digits of Charu's birth year.
- The person who likes mango is 5 years older than Visakha.
- Anko's age is either the last two digits or the reverse of the last two digits of the birth year of the person who likes mango.
- Only one person is older than Anko.
- Visakha likes apple.
- The person who likes cherry is just younger than Anko.
- The age difference between Viraj and the person who likes cherry is 24 years.
- The person who likes banana was born in an even year.
- The person who likes orange is younger than the one who likes grapes, and both ages are odd numbers.
- Monika is younger than Viraj.

Based on the above information, in which year was Monika born?

Question

Six individuals Tarun, Charu, Visakha, Monika, Anko, and Viraj were born in different years with the current base year as 2018. None of them is older than 90 years. Each person likes a different fruit: apple, orange, grapes, cherry, mango, and banana. The following conditions apply:

- The last two digits or the reverse of the last two digits of the birth year of a person can represent the age of another person. (For example, if A was born in 1943, then the age of B can be either 34 or 43.)
- Tarun was born in 1983.
- The age difference between Tarun and Charu is 21 years.
- Visakha's age is the sum of the digits of Charu's birth year.
- The person who likes mango is 5 years older than Visakha.
- Anko's age is either the last two digits or the reverse of the last two digits of the birth year of the person who likes mango.
- Only one person is older than Anko.
- Visakha likes apple.
- The person who likes cherry is just younger than Anko.
- The age difference between Viraj and the person who likes cherry is 24 years.
- The person who likes banana was born in an even year.
- The person who likes orange is younger than the one who likes grapes, and both ages are odd numbers.
- Monika is younger than Viraj.

Based on the above information, in which year was Monika born?

Accepted Answer

**Solution:**

1. Tarun was born in 1983, so his age in 2018 is:
   $$2018 - 1983 = 35$$ years.

2. The age difference between Tarun and Charu is 21 years.
   - Charu's age can be either $$35 + 21 = 56$$ or $$35 - 21 = 14$$.
   - Since none is older than 90, both are possible, but we will verify further.

3. Charu's birth year digits sum to Visakha's age.
   - If Charu is 56 years old in 2018, birth year = $$2018 - 56 = 1962$$.
     Sum of digits = 1 + 9 + 6 + 2 = 18.
   - If Charu is 14 years old, birth year = $$2018 - 14 = 2004$$.
     Sum of digits = 2 + 0 + 0 + 4 = 6.

4. Visakha's age is the sum of digits of Charu's birth year.
   - So Visakha's age is either 18 or 6.

5. The person who likes mango is 5 years older than Visakha.
   - If Visakha is 18, mango lover is 23.
   - If Visakha is 6, mango lover is 11.

6. Anko's age is either the last two digits or reverse of the last two digits of the mango lover's birth year.
   - Mango lover's age is either 23 or 11.

7. Only one person is older than Anko.
   - So Anko is the second oldest.

8. Visakha likes apple.

9. The person who likes cherry is just younger than Anko.

10. The difference between Viraj's age and the cherry lover's age is 24 years.

11. The person who likes banana was born in an even year.

12. The person who likes orange is younger than the one who likes grapes, both ages are odd numbers.

13. Monika is younger than Viraj.

**Stepwise deduction:**

- Assume Charu is 56 years old (born 1962), Visakha is 18, mango lover is 23.
- Mango lover's birth year = $$2018 - 23 = 1995$$.
- Anko's age is either 95 or 59 (last two digits or reverse of 1995).
- 95 is not possible (older than 90), so Anko is 59.
- Only one person older than Anko (59) means someone is older than 59, possibly Charu (56) is younger, so Charu cannot be 56.

- Now assume Charu is 14 (born 2004), Visakha is 6, mango lover is 11.
- Mango lover's birth year = $$2018 - 11 = 2007$$.
- Anko's age is either 07 or 70.
- 07 is too young, 70 is possible.
- Only one person older than Anko (70) means one person older than 70.

- Tarun is 35, Charu is 14, Visakha is 6, mango lover is 11, Anko is 70.
- So the oldest person is someone older than 70, possibly Viraj.

- Cherry lover is just younger than Anko (70), so cherry lover is 69.
- Viraj and cherry lover differ by 24 years:
  - Viraj's age = 69 + 24 = 93 (not possible, >90)
  - Or Viraj's age = 69 - 24 = 45 (possible)

- So Viraj is 45, Monika is younger than Viraj.

- The person who likes banana was born in an even year.

- The person who likes orange is younger than the one who likes grapes, both ages odd.

- From the above, Monika's birth year options are 1995, 2000, 2007, 2012.

- Mango lover born in 2007 (odd year), banana lover born in even year (2000 or 2012).

- Monika is younger than Viraj (45 years old, born 1973).

- Among options, 1995 fits Monika's birth year (age 23), which is younger than Viraj (45).

**Answer:** Monika was born in **1995**.

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