Direction : Study the following information carefully and answer the questions…
2019
Direction : Study the following information carefully and answer the questions given below:
Thirteen boxes of different colors are placed one above another in alphabetical order either from bottom or from top. Each box contains different number of toffees which is multiple of 13. Maximum toffees in a box is 169.
There are equal number of boxes are placed above as well as below J. Two boxes are placed between box J and the Pink colored box. Five Boxes are placed between Pink and Yellow colored box. Box which have 13 toffees is placed just below Yellow colored box. Black colored box is placed just above Red colored box and just below the box which have 169 toffees. There are as many boxes are placed above Red colored box as below the box which have 13 toffees. White colored box is placed just above the box which have 65 toffees and just below the box which have 104 toffees. There are as many boxes are placed between the boxes which have 13 and 52 toffees as between the boxes which have 52 and 104 toffees. Two boxes are placed between Blue colored box which doesn’t have 13 toffees and Green colored box which is placed just below J.
If M is Yellow colored box and sum of toffees in box O and D is equal to the sum of toffees in box H and L then, what is difference between the toffees of box L and O?
- A.
52
- B.
78
- C.
65
- D.
91
- E.
Can’t be determined
Attempted by 1 students.
Show answer & explanation
Correct answer: C
Concept
In a linear floor/stack puzzle, you do not always need the value of every single element to answer a sum-difference question. When the asked quantity is framed as a relation such as O + D = H + L, rearrange it algebraically first: the two unknown boxes (L and O) can cancel against each other, leaving the difference expressed purely in terms of boxes whose values are already FIXED by the toffee clues. So the governing idea is: pin the boxes whose toffees are forced by direct clues, then let algebra reduce the target.
Setting the stack (positions 1 = bottom to 13 = top)
Equal boxes above and below box J forces J to the exact middle, position 7. Since the boxes are named in alphabetical order from one end and box M is the Yellow box, the only consistent labelling is the consecutive block D (top) down to P (bottom): D, E, F, G, H, I, J, K, L, M, N, O, P from top to bottom.
Two boxes lie between J and the Pink box, so Pink is at position 10; five boxes lie between Pink and Yellow, so Yellow (box M) is at position 4; the box with 13 toffees sits just below Yellow, at position 3.
Black is just below the 169-toffee box and just above Red; with the 'as many boxes above Red as below the 13-toffee box' clue this fixes the 169-toffee box at the topmost position 13, which is box D.
The White box is just above the 65-toffee box and just below the 104-toffee box, so reading upward the chain 65 → White → 104 occupies three consecutive positions. Combined with the equal-spacing clue between the 13/52 and 52/104 boxes, this chain can only sit so that the 104-toffee box lands at position 9, and position 9 in the D-to-P labelling is box H. Hence box H carries 104 toffees.
Applying the relation
Box D holds 169 toffees and box H holds 104 toffees, both fixed above. Substitute into the given relation:
Start from O + D = H + L.
Replace the known boxes: O + 169 = 104 + L.
Rearrange to isolate the asked difference: L − O = 169 − 104.
Therefore L − O = 65, so the toffee difference between box L and box O is 65.
Cross-check
Notice the individual toffee counts of L and O are never needed: they cancel, and the difference depends only on the two anchored boxes D (169) and H (104). Their difference 169 − 104 = 65 is itself a valid multiple of 13 (65 = 13 × 5), consistent with the rule that every box holds a multiple of 13. Hence the answer is determinate, not 'cannot be determined', and equals 65.