One day when Ramu was going to the market with a basket full of eggs, he was hit by the hand of a person coming from the opposite direction and the basket fell down and all the eggs broke. He agreed to pay the price of the egg in Ramu's basket. Although Ramu did not know the exact number of eggs in the basket, he said the number of eggs was between 50 and 100, adding that if two eggs were counted as two and three each, nothing would be left, and if five were counted, three eggs would be left and the eggs would be sold at Rs 5 each. He calculated the amount of the egg and gave it to Ramu. How much was given to Ramu?
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Explanation:
Let eggs=x
When divided by 2,3,4,5 and 6, the remainder is always one less than the divisor
Thus, x is one less than LCM(2,3,4,5,6) OR one less than a multiple of the same.
Thus, x is one less than LCM(2,3,4,5,6) OR one less than a multiple of the same.
LCM=60
now,
x= (60-1) OR (120-1) OR (180-1)
60-1= 59
NOT divisible by 7
120-1=119
Maybe x= 119
180-1= 179
Cannot be over 150.
We can safely conclude that x= 119
The trader was carrying 119 eggs
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