Math, asked by Anonymous, 7 months ago

(5) A three digit number is equal to 17 times the sum of its digits; If the digits are
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.

Answers

Answered by richajain55
2

Step-by-step explanation:

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=17(x+y+z)

100x+10y+z = 17x + 17y + 17z100x+10y+z=17x+17y+17z

100x-17x+10y-17y+z-17z = 17x + 17y + 17z100x−17x+10y−17y+z−17z=17x+17y+17z

83x -7y -16z = 083x−7y−16z=0 -----------------------(1)

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

100x+10y+z + 198 = 100z + 10y + x100x+10y+z+198=100z+10y+x

100x- x +10y-10y +z - 100z +198 = 0100x−x+10y−10y+z−100z+198=0

99x - 99z+198 = 099x−99z+198=0

z-x=2z−x=2

z = x + 2----------------------------(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-1z+z−2=y−1

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

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

83(z-2) -7(2z-1) -16z = 083(z−2)−7(2z−1)−16z=0

83(z-2) -7(2z-1) -16z = 083(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

Answered by gyadav30122000
3

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