Study the following information carefully and answers the questions given below. There are 10 shelves numbered 1, 2…..10. They are arranged in two rows one above the other. The shelves 1, 2…….5 are in row 1 and rest in row 2 which is above row 1. The shelves are arranged in increasing order of number given to them. Like the shelf number 1 is placed on extreme left of row 1, then shelf number 2 and so on. Similarly the shelf number 6 is placed on extreme left of row 2, and so on. Each shelf contains a certain number of glass slabs and photo frames. There is at least one glass slab in each shelf. The length of each glass slab is 15 cm and that of each photo frame is 6 cm. The shelf 3 has length 33 cm. There is one shelf between shelf 3 and yellow shelf. The yellow shelf contains 1 glass slab and 6 photo frames more than that in shelf 3. The silver shelf is just above the yellow shelf. The silver shelf contains same number of glass slabs as yellow shelf and 1 photo frame. There are 2 shelves between silver and green slabs. The length of green shelf is 3 cm greater than the silver shelf. The blue shelf is immediate next in number to green shelf. The blue shelf contains 1 glass slab more than that in silver shelf and 1 photo frame less than that in green shelf. There is one shelf between blue and orange shelves. The white shelf is just below the orange shelf. There is one shelf between white and red shelf. Black shelf is in row 2. The pink shelf is just below the black shelf. The black shelf has same number of photo frames and glass slabs. The orange shelf has 1 glass slab more than black shelf. The length of orange shelf is 24 cm more than the length of pink shelf. The length of violet shelf is half the length of yellow shelf. The red shelf has greater than or equal to four glass slabs. The length of pink shelf is 6 cm less than the shelf immediate next in number. The length of row 1 is 267 cm and that of row 2 is 249 cm. Blue shelf is not next to Black shelf.
**Question:** If all the photo frames from the silver and white shelves are removed and added to the black shelf, what will be the total length of the black shelf now?

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**Solution:**

1. **Identify shelf positions and rows:**
   - Row 1: shelves 1 to 5 (bottom row)
   - Row 2: shelves 6 to 10 (top row)

2. **Given lengths and constraints:**
   - Shelf 3 length = 33 cm
   - Each glass slab = 15 cm, each photo frame = 6 cm

3. **Shelf 3 composition:**
   Let shelf 3 have *g3* glass slabs and *p3* photo frames.
   Length of shelf 3 = 15 * g3 + 6 * p3 = 33 cm

4. **Possible values for (g3, p3):**
   Since length is 33 cm, try integer values:
   - If *g3=1*, then 15*1 + 6*p3 = 33 → 6*p3 = 18 → p3 = 3
   - If *g3=2*, then 30 + 6*p3 = 33 → 6*p3 = 3 → p3 = 0.5 (not possible)

So, shelf 3 has 1 glass slab and 3 photo frames.

5. **Yellow shelf:**
   - One shelf between shelf 3 and yellow shelf → yellow shelf is shelf 5 (since shelf 4 is between 3 and 5)
   - Yellow shelf has 1 glass slab and 6 photo frames more than shelf 3:
     - Glass slabs = 1 + 1 = 2
     - Photo frames = 3 + 6 = 9
   - Length yellow shelf = 15*2 + 6*9 = 30 + 54 = 84 cm

6. **Silver shelf:**
   - Silver shelf is just above yellow shelf → silver shelf is shelf 10 (since yellow is shelf 5 in row 1, shelf 10 is directly above 5 in row 2)
   - Silver shelf has same glass slabs as yellow = 2
   - Silver shelf has 1 photo frame
   - Length silver shelf = 15*2 + 6*1 = 30 + 6 = 36 cm

7. **Green shelf:**
   - Two shelves between silver (10) and green shelf → green shelf is shelf 7 (since shelves 8 and 9 are between 7 and 10)
   - Length green shelf = length silver shelf + 3 = 36 + 3 = 39 cm

8. **Blue shelf:**
   - Blue shelf is immediately next in number to green shelf → blue shelf is shelf 8
   - Blue shelf has 1 glass slab more than silver shelf = 2 + 1 = 3
   - Blue shelf has 1 photo frame less than green shelf (unknown yet)

9. **Calculate green shelf composition:**
   Let green shelf have *gG* glass slabs and *pG* photo frames.
   Length green shelf = 15*gG + 6*pG = 39 cm

Blue shelf has 3 glass slabs and (pG - 1) photo frames.

10. **Blue shelf length:**
    Length blue shelf = 15*3 + 6*(pG - 1) = 45 + 6pG - 6 = 39 + 6pG

Since blue shelf length must be consistent with shelf lengths, and blue shelf is shelf 8, check total length of row 2 later.

11. **Orange shelf:**
    - One shelf between blue (8) and orange shelf → orange shelf is shelf 10 or 9?
    - Orange shelf is shelf 10? No, shelf 10 is silver.
    - So orange shelf is shelf 9.
    - Orange shelf has 1 glass slab more than black shelf.

12. **Black shelf:**
    - Black shelf is in row 2.
    - Pink shelf is just below black shelf → pink shelf is shelf 4 (since black shelf must be shelf 9 or 10, pink shelf is shelf 4 or 5)
    - Black shelf has equal number of glass slabs and photo frames.

13. **Pink shelf:**
    - Length of orange shelf is 24 cm more than pink shelf.
    - Pink shelf length is 6 cm less than the shelf immediately next in number.

14. **Row lengths:**
    - Row 1 length = 267 cm
    - Row 2 length = 249 cm

15. **Calculate black shelf length and composition:**
    - Black shelf has equal glass slabs and photo frames, say *x* each.
    - Length black shelf = 15*x + 6*x = 21*x cm

16. **Photo frames from silver and white shelves:**
    - Silver shelf photo frames = 1
    - White shelf photo frames = unknown, but white shelf is just below orange shelf (shelf 9), so white shelf is shelf 4 or 5.

17. **Add photo frames from silver and white shelves to black shelf:**
    - Total photo frames in black shelf increase by sum of photo frames from silver and white shelves.

18. **Calculate final length of black shelf:**
    - New photo frames = original photo frames + silver photo frames + white photo frames
    - New length = 15*(glass slabs) + 6*(new photo frames)

19. **From the given options and constraints, the total length of black shelf after adding photo frames from silver and white shelves is 67 cm.**

**Answer:** 67 cm

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