Question
The greatest number of four digits which when divided by
10, 12, 14 leave remainders 5, 7, 9 respectively is:Solution
The difference between divisor and the corresponding remainder is equal (i.e 5). LCM of 10, 12 and 14 = 420 Largest 4-digit number = 9999 After dividing 9999 by 420 we will get the remainder as 339. Therefore, the number divisible by 420 = 9999 – 339 = 9660 If 5 is subtracted from the number 9660 the resulting number will follow the condition in the question and that number is 9655.
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