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 egg left.If the capacity of the basket is 100 eggs, find how many eggs are in the basket? Explain with reasoning

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Solution

$Since, the capicity of the basket is 100 eggs, therefore the number of eggs in the basket is less than or equal to 100 . When the trader sells 7 eggs at a time, there are no eggs left in the box . So the number of eggs in the box is multiple of 7 . The multiples of 7 which are less than or equal to 100 are; 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98 Now, if the trader sells 4 eggs at a time, there is only 1 egg left in the basket . So the number of eggs in the basket is one less than a multiple of 4 . The number of eggs satisfying this condition is : 21, 49, 77 Also, if the trader sells 3 eggs at a time, there is only 1 egg left in the basket . So the number of eggs in the basket is one less than a multiple of 3 . The number of eggs satisfying this condition is 49 . Hence, the required number of eggs in the basket is 49 .$

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