Question

three digit is equal to 17 times the sum of the digits. If the digit are revsered the new number is 198 more than the original number. The sum of the extreme digit is 1 less than the middle digit.find the roiginal number.​

Answer 1

Answer:

let the digit in hundreds place be x

let the digit in unit place be y

let the original number be 100x+10(x+y+1) +y

100x + 11y+10

Interchange number be 11x + 110y + 10

As per first condition

Given number= 17 x( sum of the digit)

100x + 11y +10= 17x (2x+2y+1)

100x +11y +10= 34x+34y+17

76x-23y=7 (1)

As per second condition

given number+198= 110y+11x+10

99x-99y=-198

x-y=-2

x=y-2 (11)

76(y-2) -23=7

76-152-23y=7

53y=159

y=3

substitute y=3 in equation (11)

x=y-2

x=3-2

x=1

Original number= 110x+11y+10

110(1) +11(3) +10

110+33+10

153