Question

the digit of a two digit number differ by 5 if the digits are interchanged and resulting number is added to the original number we get 99 find the original number

Answer 1

Let the one digit number be x
And tens digit number be y
(y>x)
No. 10y+x
And interchanged no. =10x+y

According to the question,

x-y=5.............¡
10y+x+10x+y=99
=>11y+11x=99
=>x+y=9..........¡¡

Now ¡¡-¡ we get,
x+y-(x-y) =9-5
=>2y=4
=>y=2
Putting y=2in equation ¡
x-y=5
=>x-2=5
=>x=7

The number is
10y+x=10×2+7=27

Answer 2

Answer:

Let the one digit number be x

And tens digit number be y

(y>x)

No. 10y+x

And interchanged no. =10x+y

According to the question,

x-y=5.............¡

10y+x+10x+y=99

=>11y+11x=99

=>x+y=9..........¡¡

Now ¡¡-¡ we get,

x+y-(x-y) =9-5

=>2y=4

=>y=2

Putting y=2in equation ¡

x-y=5

=>x-2=5

=>x=7

The number is

10y+x=10×2+7=27