Question

a three digit number is equal to 17 times the sum of its digits are reversed the new number is 198 more than the old number. also the sum of extreme digits is less than the middle digits by unity find the original number

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Answer 1

let the hundred place digit be x , tens digit be y and unit digit be z

So Number = 100x+10y+z

We are given that A three digit number is equal to 17 times the sum of its digit

-----------------------(1)

if the digits reversed, the new number is 198 more than the old number

the sum of extreme digits is less than the middle digit by unity.

And,

z + x = y-1

By putting (2)

y = 2z-1 ----------------------------(3)

Putting (3) and (2) in (1) we get

z = 3

put z = 3 in (3)

y = 2(3) -1

y = 5

Put z = 3 in (2)

x = 3-2=1

So. number = 100(1) + 10(5) + 3 = 153

So, number = 153

Hence the number is