Question

Sum of digits of a two digit number is 9 . When the digits are interchanged new number is greater than the original number by 9. Find the original number.



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Answer 1

Answer:

45

Step-by-step explanation:

let the 2 digits be x and y

=> the number is 10x+y

given,

x + y = 9 ------------------------- >  1

also , if digits interchanged the new number will 9 greater than 10x+y

ie, 10y+x = 9+ 10x+y

=> 10y-y+x-10x = 9

=> 9y - 9x = 9

=> y-x =1 ------------------------------ 2

solving eqn.s 1 & 2 , we get

x + y = 9

x - y = -1

------------

2x    = 8

=>x= 8/2 = 4

substitute the value of x in 1 ,we get

4 + y = 9

=>  y = 9-4 = 5

Solution : x=4 and y=5

therefore the original number is 10(4)+5 = 40+5 = 45

verification :

sum of digits = 4+5 = 9 (first condition satisfied)

difference between the new number and original no. = 9

ie, 54 - 45 = 9 (second condn. satisfied)

Answer 2

let the digits be x and y respectively

hence,x+y=9

x=9-y

the original number=10×(9-y)+y

=90-9y

after interchanging

ten's place=y and one's place=9-y

interchanged number=10×y+9-y

=9y+9

A/q

9y+9=90-9y+9

9y+9=99-9y

9y+9y=99-9

18y=90

y=90/18

so,y=5

original number=9-y y

=45