Question

A three-digit integer is reversed to form another three-digit integer. The positive difference between the two numbers is 396. What is the greatest possible value for the original integer?

Answer 1

The original greatest possible value is 985 .

Explanation:

Given as :

The statement as

A three-digit integer is reversed to form another three-digit integer.

Let The original three digit number = zyx

i.e The original three digit number = 100 z + 10 y + x

Again'

The another three digit number after reversing = xyz

I.e The another three digit number after reversing = 100 x + 10 y + z

Again

The difference between number = 396

So, ( 100 z + 10 y + x) - ( 100 x + 10 y + z) = 396

Or, 100 (z - x) + (10 y - 10 y) + ( x - z) = 396

Or, 100 (z - x) + 0 + (x - z) = 396

Or, 99 (z - x) = 396

Or, z - x = 4

y can take between 0 to 9 i.e
`\geq` 10 values

but z can not be 0

Reverse numbers also start with three digits

x max 5

So, z max = 5 + 4 = 9

So, The value of y be 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8

for greatest possible take y as 8

So, the number = 985

Hence, The original greatest possible value is 985 . Answer