A trader with a basket of eggs finds that if he sells 3 eggs at a time there is only 1 egg left. If he sells 4 eggs at a time there is again 1 egg left. However, if the trader 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? Explain with reasoning.

The L.C.M of 3 and 4 is 12

The maximum capacity of the egg basket is 100.

We will make the list of multiples of 12 > 100

These are 12, 24, 36, 48, 60, 72, 84, 96

Since 1 egg is left if he sells 3 or 4 eggs we will add 1 to each number in the above list,

The new list is as follows

13, 25, 37, 49, 61, 73, 85, 97 ……(1)

According to the condition given in the question, when 7 eggs are selected, no eggs remain.

⇒ the exact number of eggs would be divisible by 7 exactly

From list 1 we find only number 49 matches all the conditions

Hence the number of eggs in the basket is 49 eggs.