Question

The digits of a positive number have 3digits which are in A.P. and their sum is 18.

The number obtained by reversing digits is 594 less than the original number.

Find the number.

Answer 1

The answer is 963.

The sum of the digits is 18.

Let the digits be a-d,a ,a+d.

where d is the difference between the digits.

a-d+a+a+d=18.

3*a=18

a=6.

Now by reversing the number,it is 594 less than the original.

The original number is

(6-d)*100+6*10+ (6+d).

and the number reversed is

(6+d)*100+6*10+(6-d).

now,

(6-d)*100+6*10+(6+d)-594= (6+d)*100+ 6*10+(6-d)

By simplifying,

-198 *d= 594

d=-3.

so the digits are 9,6,3

and the number is 963