Question

The sum of a digit of a two digit number is 9.if nine is added to the number the number get reversed find the number

Answer 1

Answer:

Step-by-step explanation:

In a two-digit number, the sum of the digits is 9. If the digits are reversed, the number is increased by 9. What is the number?

Let m and n be the two digits. Then:

m+n=9

10m+n+9=10n+m

n=9-m

Then:

10m+(9-m)+9=10(9-m)+m

9m+18=90–9m

18m=72

m=4

n=5

The number is 45

Answer 2

let the tens digit be x

the ones digit be y

then the no. is 10x+y

also if the no. is reversed the no. become 10y+x

A.T.Q

x+y=9 ....... (1)

given if nine is added to the number the number get reversed

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

10x-x+y-10y+9=0

9x-9y=-9

9 (x-y)=-9

x-y=-1 ...... (2)

(1)+(2)

x+y+x-y=9-1

2x=8

x=4

putting x=4 in (1)

4+y=9

y=5

hence the no. is 10x+y

10×4+5

=>45

ANS = the no. is 45