Tittle - Find the minimum number of apples in the carton?

Minimum of 12 apples

Explanation :  

Let the number of children be X,
Therefore, the number of apples bought by Tanya = ( X + 1) 
The total number of apples in the shop A = ( X + 1) 
Total number of apples bought by Trader Tarun =  2( X + 1 ) 
Total number of apples in the carton = 4( X + 1 ) 

Now, the minimum no. of apples in a carton: 
We assume:  X is not equal to 0  
X is not equal to 1 ( Tanya has children not a single child)  
X  equal to 2  (Tanya has a minimum of 2 children) 

When X = 2
Let the number of children be X
Therefore, the number of apples bought by Tanya = ( X + 1)
The total number of apples in the shop A = ( X + 1)
Total number of apples bought by Trader Tarun = 2( X + 1 )
Total number of apples in the carton = 4( X + 1 )
Now, minimum no of apples in carton:
We assume:
X is not equal to 0
X is not equal to 1 ( Tanya has children not a single child)
X equal to 2 (Tanya has a minimum of 2 children)
When X = 2
4( X + 1 )
= 4( 2 + 1 )
= 12
Thus, minimum of 12 apples