Question

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

Answer 1

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 . 

Answer 2

[Answer:- 49 eggs.]

Solution:- A shopkeeper with a basket of eggs finds that if he sells 3 eggs at a time there is only one egg left if he sells four eggs at a time there is again 1 egg left however if the trader sells 7 is at a time there is no egg left is the capacity of the basket is 108

LCM of 3 and 4 = 3×4 = 12

The capacity of the basket is 100.

So, there may be:-

= 12 × 8 +1

= 96 + 1

= 97 eggs.

But, 97 is not divisible by 7.

Again, there may be:

12 × 7 +1 = 85 eggs.

12 × 6 +1 = 73 eggs.

12 × 5 +1 = 61 eggs.

12 × 4 +1 = 49 eggs.

Among these numbers 85 , 73 and 61 are not divisible by 7. But 49 is divisible by 7.

So, the number of eggs in the basket is 49.