Eight individuals A, B, C, D, E, F, G, and H are employed in a company across three departments — Production, Management, and Finance — holding two types of posts: Manager and General Manager. Each person has a unique whole number age. The following information is given:

- E's age is twice that of C.
- A is 53 years old and works in Production.
- The employees whose combined age totals 100 years work in Finance as General Managers.
- F works in Production.
- B works in Management but not in the same department as D, and B and D hold different posts.
- H and G hold the same post but do not work in Production.
- H and F hold different posts.
- No more than two persons hold the same post within the same department.
- E and A work in the same department but hold different posts.
- A and D hold different posts.
- The sum of the ages of C and G is 64 years.
- C and D are Managers but in different departments, neither in Production.
- E is 12 years older than F and 12 years younger than H.
- The difference between the ages of C and D equals H's age.
- B is 30 years old, which is half of H's age.

**Question:** How many persons are working as Managers?

Question

Eight individuals A, B, C, D, E, F, G, and H are employed in a company across three departments — Production, Management, and Finance — holding two types of posts: Manager and General Manager. Each person has a unique whole number age. The following information is given:

- E's age is twice that of C.
- A is 53 years old and works in Production.
- The employees whose combined age totals 100 years work in Finance as General Managers.
- F works in Production.
- B works in Management but not in the same department as D, and B and D hold different posts.
- H and G hold the same post but do not work in Production.
- H and F hold different posts.
- No more than two persons hold the same post within the same department.
- E and A work in the same department but hold different posts.
- A and D hold different posts.
- The sum of the ages of C and G is 64 years.
- C and D are Managers but in different departments, neither in Production.
- E is 12 years older than F and 12 years younger than H.
- The difference between the ages of C and D equals H's age.
- B is 30 years old, which is half of H's age.

**Question:** How many persons are working as Managers?

Accepted Answer

**Solution:**

1. From the given data, B is 30 years old and his age is half of H's age, so:
   $$H = 2 	imes 30 = 60$$

2. E is 12 years younger than H, so:
   $$E = 60 - 12 = 48$$

3. E is 12 years older than F, so:
   $$F = 48 - 12 = 36$$

4. A is 53 years old and works in Production.

5. E and A work in the same department but hold different posts.

6. The sum of ages of C and G is 64:
   $$C + G = 64$$

7. E's age is twice C's age:
   $$E = 2 	imes C ightarrow 48 = 2C ightarrow C = 24$$

8. Using $C=24$, find $G$:
   $$G = 64 - 24 = 40$$

9. The difference between ages of C and D equals H's age:
   $$|D - C| = H = 60$$

Since $C=24$, possible $D$ values are:
   $$D = 24 + 60 = 84 	ext{ or } 24 - 60 = -36 	ext{ (not possible)}$$

So, $D = 84$.

10. B and D work in different departments and hold different posts.

11. C and D are Managers but in different departments, neither in Production.

12. Persons whose total age is 100 years work in Finance as General Managers.

Let's find pairs summing to 100:
   - $B(30) + ? = 100 ightarrow ? = 70$ (no one with age 70)
   - $F(36) + ? = 100 ightarrow ? = 64$ (no one with age 64)
   - $G(40) + ? = 100 ightarrow ? = 60$ (H is 60)

So, $G$ and $H$ work in Finance as General Managers.

13. H and G hold the same post (General Manager) and are not in Production.

14. F works in Production, and H and F hold different posts.

15. A and D hold different posts.

16. E and A work in the same department but different posts.

17. C and D are Managers.

18. Summarizing posts:
   - Managers: C, D, B (B is in Management, different from D's department, and B and D hold different posts, so B is likely Manager)
   - General Managers: G, H (Finance)
   - A and E in Production, different posts (one Manager, one General Manager)
   - F in Production, post different from H (who is General Manager in Finance), so F's post is Manager or General Manager in Production.

19. Counting Managers:
   - C (Manager)
   - D (Manager)
   - B (Manager)
   - A or E or F (one of them is Manager in Production)

Since A and E are in the same department with different posts, and F is also in Production, and no more than two persons hold the same post in the same department, only one of A, E, F can be Manager.

20. Therefore, total Managers = 4.

**Answer:** Four

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