Hi Aditya,
What were you not able to understand? Can you please be more specific.

I did not understnd the solution from the point where it says "remaining 3 oranges can be in any boxes. . . . . . . . "

Hi Aditya,
We have improved the solution. Please go through it. Feel free to follow us for further doubts.

Hi Tilak,
This is the only way to solve this question. We have now put up a clearer explanation for your understanding. Please refer to it.

We have to minimize the number of boxes having same number of oranges. We have 128 boxes but there are only 25 distinct number of oranges which can be there in any box. So we first divide these numbers equally. So Out of 128 boxes, sets of 5 boxes contain the same number of oranges. 3 additional boxes are remaining. In order to minimize the same number of oranges in any box, these three should contain distinct number of oranges. Thus, there will be at least 6 boxes having same number of oranges.

Hi Shresth, we have edited the question and made it clearer. Please check it now.

Hi jeet,
I will try to break the question to make you understand
First part says, what is the maximum number of boxes with same number of oranges.
This can be 128
Second part says what is the minimum possible case of this.
If we need to minimize this then we need to distribute all of them uniformly
So 5*25=125 i.e. there are 5 boxes containing 120, 121, ... 144 oranges
The rest 3 can have any number of oranges
Hence, there are 6 boxes containing {3 among 120, 121,...144} number of oranges in each
This is the minimum possible value for most boxes with same number of oranges
Hope this clarifies your doubt:) 

Hi shreejita,
I have updated the question
Try it out now

Hi Suraj,

We need to find the minimum value of x, where x is the maximum number of boxes containing the same number of oranges. When you distribute 3 oranges then 3 boxes will have 6 oranges, and in some boxes, we have 5 oranges. Hence 6 will be maximum in this case and minimum when the distribution is even.

Hope this helps.

Hi Somyadeep,
I am sorry, but I cannot comprehend your doubt.
So, let me explain the solution for a better understanding.
We know that there are 128 boxes.
Now, we can fill 25 different values in each box(at least 120 and at most 144).
Thus, we will be able to fill 125(25*5) boxes, with each value getting repeated 5 times.
For the rest 3 boxes, we will fill in three different values(it can be any value).
As each value has been repeated 5 times before, three values will be repeated 6 times.
Hope this helps. Please let us know if your doubt were cleared.
Regards