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.

Asked by  | 28th Feb, 2013, 10:08: PM

Expert Answer:

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

Answered by  | 1st Mar, 2013, 09:17: AM

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