Question

the sum of the a two - digit number is 9.if 9 is added to a number formed by reversing the digits, then the result is thrice of the original number.finf the original number​

Answer 1

Answer:

Step-by-step explanation:

Let the digit in units place be x and digit in ten's place be y

x+y = 9 ; x = 9-y

Original number = 10y +x

New number = 10x+y+9

10x+y+9=3(10y+x)

10x+y+9= 30y+3x

10x-3x+9= 30y-y

7x+9=29y

7x+9-29y = 0

7(9-y) +9-29y = 0

63-7y+9-29y = 0

72-36y = 0

72=36y

y= 72/36

y=2

x+y = 9

x+2 = 9

x=9-2=7

Original number = 10y+x =10(2) +7= 27

Answer 2

Answer:

Let the unit place be ‘x'

Tenth place be y

The number is 10y+x

x+y = 9 (according to the condition) (1)

Digits are interchanged Unit place' y ‘& tenth place ‘ x'

New no is 10x +y

This is 9 more than the original number

10x+ y = 10y+x +9

10x-x+y-10y = 9

9x-9y= 9

x-y = 1 (dividing by 9) (2)

Adding the two equations

2x = 10

x= 5

Substituting the value of x in first equation

y = 4

The number is 45, the original number is 54 this is 9 more of the new number.

Ans :45