Ashopkeeper 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.

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.

[Answer = 49]