Six persons C, D, B, O, N, and P are sitting in a row facing north. Their ages are 6, 12, 15, 18, 27, and 36 years but not necessarily in the same order. The following conditions are given:

1. C sits 3rd from one of the ends.
2. The one who is 12 years old sits 2nd to the right of C.
3. The number of persons sitting to the right of the one who is 12 years old is the same as the number of persons sitting to the left of D.
4. O sits 2nd to the right of the one who is 6 years old.
5. Two persons sit between D and B, whose age is twice that of D.
6. N sits to the right of P.
7. The one who is 36 years old sits 3rd to the left of the one who is 15 years old.
8. The age of O is 18 years.

What is the total age of C and B?

Question

Six persons C, D, B, O, N, and P are sitting in a row facing north. Their ages are 6, 12, 15, 18, 27, and 36 years but not necessarily in the same order. The following conditions are given:

1. C sits 3rd from one of the ends.
2. The one who is 12 years old sits 2nd to the right of C.
3. The number of persons sitting to the right of the one who is 12 years old is the same as the number of persons sitting to the left of D.
4. O sits 2nd to the right of the one who is 6 years old.
5. Two persons sit between D and B, whose age is twice that of D.
6. N sits to the right of P.
7. The one who is 36 years old sits 3rd to the left of the one who is 15 years old.
8. The age of O is 18 years.

What is the total age of C and B?

Accepted Answer

**Solution:**

Let's analyze the clues step-by-step and arrange the persons and their ages accordingly.

1. **C sits 3rd from one of the ends.**
   - Since there are 6 persons, positions are numbered 1 to 6 from left to right.
   - C can be at position 3 (3rd from left end) or position 4 (3rd from right end).

2. **The one who is 12 years old sits 2nd to the right of C.**
   - If C is at position 3, then 12-year-old is at position 5.
   - If C is at position 4, then 12-year-old is at position 6.

3. **The number of persons sitting to the right of the one who is 12 years old is the same as the number of persons sitting to the left of D.**
   - Let's check both cases:
     - Case 1: 12-year-old at position 5
       - Persons to right of 12-year-old = 6 - 5 = 1
       - So, persons to left of D = 1 → D is at position 2
     - Case 2: 12-year-old at position 6
       - Persons to right of 12-year-old = 0
       - So, persons to left of D = 0 → D is at position 1

4. **O sits 2nd to the right of the one who is 6 years old.**
   - If 6-year-old is at position x, O is at position x + 2.

5. **Two persons sit between D and B, whose age is twice that of D.**
   - The distance between D and B is 3 positions.
   - So if D is at position d, B is at position d + 3 or d - 3.

6. **N sits to the right of P.**
   - Position of N > Position of P.

7. **The one who is 36 years old sits 3rd to the left of the one who is 15 years old.**
   - If 15-year-old is at position p, 36-year-old is at position p - 3.

8. **The age of O is 18 years.**

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**Try Case 1: C at position 3, 12-year-old at position 5, D at position 2**

- Positions: 1, 2(D), 3(C), 4, 5(12-year-old), 6

- From clue 5: Two persons between D(2) and B → B at position 5 or position -1 (not possible)
  - B at position 5 (which is 12-year-old)

- B's age is twice D's age.
  - Let D's age = x, then B's age = 2x.
  - B is 12 years old, so 2x = 12 → x = 6
  - So D is 6 years old.

- From clue 4: O sits 2nd to the right of 6-year-old.
  - 6-year-old is D at position 2.
  - O is at position 4.

- O's age is 18 years (given).

- From clue 7: 36-year-old sits 3rd to the left of 15-year-old.
  - Possible positions for 15-year-old:
    - Position 6 (then 36-year-old at 3)
    - Position 5 (then 36-year-old at 2)
  - Position 5 is 12-year-old (B), so 15-year-old can't be 5.
  - Position 6 is free, so 15-year-old at 6, 36-year-old at 3.

- Assign ages:
  - Position 3 (C) = 36 years
  - Position 6 = 15 years

- From clue 6: N sits to the right of P.
  - Positions left: 1 and 5
  - Position 5 is 12-year-old (B), so P and N must be at 1 and 5.
  - N must be to the right of P, so P at 1, N at 5.

- Remaining ages: 27 years (since 6, 12, 15, 18, 36 assigned)
  - Assign 27 to P at position 1.

**Final arrangement:**

| Position | 1  | 2 (D) | 3 (C) | 4 (O) | 5 (N/B) | 6 |
|----------|----|-------|-------|-------|---------|---|
| Person   | P  | D     | C     | O     | B (N)   | ? |
| Age      | 27 | 6     | 36    | 18    | 12      | 15|

- N is at position 5 (B), so N = B.

**Total age of C and B:**

- C = 36
- B = 12
- Sum = 36 + 12 = 48

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**Answer:** 48

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