Question
The digits of a three-digit number are in
A.P. and their sum is 15 . If the number formed by reversing the digits is 198 more than the original number, what is the original number?
Solution
ATQ, Let the digits be: First = 5 - d Second = 5 Third = 5 + d Since sum = 15, middle digit = 15/3 = 5 Original number = 100(5 - d) + 10(5) + (5 + d) = 500 - 100d + 50 + 5 + d = 555 - 99d Reversed number = 100(5 + d) + 50 + (5 - d) = 500 + 100d + 50 + 5 - d = 555 + 99d Given reversed number is 198 more than original: (555 + 99d) - (555 - 99d) = 198 198d = 198 d = 1 Original number = 555 - 99 = 456
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