Question

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

Answer 1

Step-by-step explanation:

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Let the two digit number be xy

x+y=9

yx+9=3(xy)

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

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

29x=7y+9

y=9−x

29x=7(9−x)+9

36x=63+9

36x=72

x=2

x+y=9

y=9−2=7

Original number =27

Answer 2

Answer:

x=1,y=8 and the no. will be 18

Step-by-step explanation:

Let the first no. be x.

Let the second no. be y.

The no. will be = 10x+y

After reversing the no. be=10y+x  

A.T.Q : x+y = 9   …1

9(10y+x)=2(10x+y)

90y+9x=20x+2y

90y-2y=20x-9x

88y=11x

88y-11x=0

11(8y-x)=0

8y-x=0    …2

Add equ. 1 and 2,we get

x+y+8y-x= 0+9

9y=9

Y=1

Put the value of y in equ.1 we get

x+1=9

x=9-1

x=1

x=1,y=8