Question

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,again 1 egg is 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.

Answer 1

49 is the answer highest number of eggs

Answer 2

The capicity of the basket is 100 eggs, therefore the number of eggs in the basket is less than or equal to 100.When the trader sells 7 eggs at a time, there are no eggs left in the box.So the numberof eggs in the box is multiple of 7.The multiples of 7 which are less than or equal to 100

are;7,14, 21,28,35, 42 ,49,56,63, 70, 77, 84, 91 ,98

Now, if the trader sells 4 eggs at a time, there is only 1 egg left in the basket.So the numberof eggs in the basket is one less than a multiple of 4.The number of eggs satisfying this condition is: 21,49,77

Also, if the trader sells 3 eggs at a time, there is only 1 egg left in the basket.So the numberof eggs in the basket is one less than a multiple of 3.The number of eggs satisfying this condition is 49.

Hence, the required number of eggs in the basket is 49