Question

A number consists of three digits , the right hand digit being zero . If the left hand and the middle digits be interchanged the number is diminished by 180. If the left hand digit be halved and the middle and roght hand digits be interchanged the number is diminished by 454 . Findthe Number

Answer 1

let x be in hundred place

y be in tens place

third digit is 0 so dont mind it

original number =100x+10y

as per first condition new number

2nd digit becomes first digit

so new number =100y + 10x + 0

EQUATION 1

100x + 10y-180=100y+10x

simplifying we get 90x - 90y=180

90(x - y)=180

x-y=180/90=2

as per second condition new number

fiest digit gets halfed

100x/2=50x

next 2nd digit becomes 1st and viceversa

so 0+1*y

EQUATION 2

100x + 10y -454=50x + y

simplifying we get 50x + 9y=454

third step = multiply 50 in equation 1

so50(x - y)=50*2

50x-50y=100

next subtract thirs step from equation 2

50x + 9y=454

--------

50x-50y=100

___________

0+ 59y =354

we get 59y=354

so y = 6

putting this value to equation 1 we get x as 8

so original number

100x+10y = 800 + 60=860