Question

A shopkeeper with a basket of apple finds that if he sells 3 apples at a time there is only one apple left if he sells four apple at a time there is again 1 apple left however if the trader sells 7 apple is at a time there is no apple left is the capacity of the basket is 108 apples then find how many days are there in the basket explain with reasoning. ​

Answer 1

Who was that shopkeeper

I'll go, ask him n tell u the ans

Answer 2

Answer : 

If our number of apple is divisible by  3 and 4  , than that number we can get by LCM of these numbers  , So 

So LCM ( ​  3 and  4  )  =  2 × 2 × 3  = 12

And here when we divide that number of apple by ​3 and  4  we get 1 as remainder so our number of eggs could be 12 + 1 = 13

Or Just the multiple of 12 +  1 
So
That number could be 

12 × 1  + 1  =  13
12 × 2  + 1  = 25
12 × 3  + 1  = 37 
12 × 4  + 1  = 49
12 × 5  + 1  = 61
12 × 6  + 1  = 73
12 × 7  + 1  = 85
12 × 8  + 1  = 97   

And as the capacity of the basket is 108 apple , SO our number of apple could be one of those number written above

And as our number of apple   is divisible by 7 , so that number is also a multiply of 7  , 
So that number could be 

7 × 2  =  14
7 × 3 = 21
7 × 4 = 28
7 × 5 = 35
7 × 6 = 42
7 × 7 = 49
7 × 8 = 56
7 × 9 = 63
7 × 10 = 70
7 × 11 = 77
7 × 12 = 84
7 × 13 = 91
7 × 14 =98
7 × 15 = 105
..... 

Here we can see that 49 number is common in both the arrangement . 

So our number of apple   is 49  , that gives 1 as remainder after division by ​​ 3 and 4  and there will be no remainder if 49 divide by 7 .