Question

A man sells a basket of egg and finds that he sells 3 eggs at a time there's only 1 egg left.If she sells 4 eggs at a time,there I again 1 egg left .If he sells 7 eggs at a time,there are no eggs left.If the capacity of the basket is 100 eggs, find how many eggs are in the basket.

Answer 1

Answer :

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


So LCM ( ​ 3 and 4 ) = 2 $\times$ 2 $\times$ 3 = 12

And here when we divide that number of eggs 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 $\times$ 1 + 1 = 13
12 $\times$ 2 + 1 = 25
12 $\times$ 3 + 1 = 37
12 $\times$ 4 + 1 = 49
12 $\times$ 5 + 1 = 61
12 $\times$ 6 + 1 = 73
12 $\times$ 7 + 1 = 85
12 $\times$ 8 + 1 = 97

And as the capacity of the basket is 100 eggs , SO our number of eggs could be one of those number written above

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

7 $\times$ 2 = 14
7 $\times$ 3 = 21
7 $\times$ 4 = 28
7 $\times$ 5 = 35
7 $\times$ 6 = 42
7 $\times$ 7 = 49
7 $\times$ 8 = 56
7 $\times$ 9 = 63
7 $\times$ 10 = 70
7 $\times$ 11 = 77
7 $\times$ 12 = 84
7 $\times$ 13 = 91
.....

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

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