Question
Thu February 28, 2013 By:
 

The digits of a 3 digit no. are in A.P. and their sum is 15.The no. obtained by reversing the digits is 396 less than the original no.Find the no.

Expert Reply
Fri March 01, 2013
Let the digits of the number be x-d (hundredth place), x (tenth place) and x+d (ones's place) where d is the common differnece of the AP. 
 
So, x-d+x+x+d = 15
i.e. 3x = 15
x = 5
 
Also, the number obtained by reversing the digits is 396 less than the original number
i.e. Original number = Number obtained by reversing the digits +396
So, (x-d)100 + 10x + (x+d) = (x+d)100 + 10x + (x-d) + 396
101x - 99d = 101x+99d + 396
-198d = 396
d = -2
 
So, the digits are 7,5,3 and hence, the number is 753

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