Question

A number consists of three digits the right hand 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 right hand digits be interchanged the number is diminished by 454 . find the 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



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