Question

There are a certain no. of apples in a basket. If the number of apples are divided among 8 people, 3 apples are left out and if the same no. of apples are divided among 6 people, 1 apple is left out. Find the maximum possible no. of apples in the basket if the capacity of the basket is 500.
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Answer 1

8A+3 = 6B+1
Since, 8-3 = 6-1 = 5, so minimum no. of apples in the basket = LCM(8,6) - 5 = 43
So, the required no.of apples in the basket will be of the form 48k + 43.
Therefore, maximum possible no. of apples in the basket (when k=9) = 48x9 + 43 = 475.