Question

A number of two digits is decreased by 9 when the digits are interchanged. The sum of the two digits is 9. Find the number

Answer 1

let x be a 2 digit no.

let a be digit at ones place

and b at 10s place

therefore, x=a+10b................1

also digits get interchanged when no. is decreased by 9

i.e x-9=b+10a..............2

also a +b=9

i.e b = 9-a..........3

putting =n 3 in=n 2 we get

x-9=9-a+10a

or x-9+9=-a+10a

or x=9a...........4

put =n 4 in =n 1 we get

9a=a+10b

or 9a-a=10b

or 8a=10b

or a= 10b/8; a=1.25b..............5

put =n 5 in=n 3

b=9-1.25b

9 =2.25b

b = 4...................6

put b=4 in 5

a= 1.25×4

a= 5..................7

put =ns 6 &7 in =n 1 we get

x= 4 + 10×5

x=4+50

x=54

therefore the no. is 54