A three digit number is equal to 17 times

Asked by admin @ 17/08/2021 in Math viewed by 331 People

A three digit number is equal to 17 times the sum of its digit; if the digits reversed, the new number is 198 more than the old number; also the sum of extreme digits is less than the middle digit by unity. find the original number by using the method of linear ewuation in two variables

Answered by admin @ 17/08/2021

Answer:

153

Step-by-step explanation:

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

$100x+10y+z = 17(x+y+z)$

$100x+10y+z = 17x + 17y + 17z$

$100x-17x+10y-17y+z-17z = 17x + 17y + 17z$

$83x -7y -16z = 0$ -----------------------(1)

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

$100x+10y+z + 198 = 100z + 10y + x$

$100x- x +10y-10y +z - 100z +198 = 0$

$99x - 99z+198 = 0$

$z-x=2$

$z = x + 2----------------------------(2)$

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

And,

z + x = y-1

By putting (2)

$z+z-2=y-1$

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

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

$83(z-2) -7(2z-1) -16z = 0$

$83(z-2) -7(2z-1) -16z = 0$

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 153

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