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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 February 2013, 10:08 PM
Answered by 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 Expert 1st March 2013, 9:17 AM
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