Question
A shopkeeper sells apples. He sells x% of the stock each
day and x/5% of the remaining apples gets spoiled overnight, then he sells the remaining apples the next day. This cycle continues for 2 nights. The shopkeeper did not add up any new stock. If 290 apples gets spoiled over 2 nights, the find the number of apples shopkeeper has in stock on the start of the first day, if the value of x is the integral root of the equation 9x² – 418x – 1600 = 0?Solution
Let, the initial stock of the apples = a units 
Since x is an integer, so, x = 50 Therefore, we can now say that he sells 50% of apples each day and 10% of the remaining apples gets spoiled overnight. So, according to the question, we can make the following table 
Total number of apples that gets spoiled = 0.05a + 0.0225a = 290 0.0725a = 290 a = 4,000 Hence, option b) is the correct answer.
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