Question

a two digit number is 3 more than 4 times the sum of its digits.if 18 is added to the number it's digits are interchanged find the number​

Answer 1

Step-by-step explanation:

10x+y=4(x+y)+3

10x+y+18=10y+x

10x+y=4x+4y+3

6x-3y-3=0

2x-y-1=0----1

9x-9y+18=0

x-y+2=0------2

1-2

2x-y-1=0

-(x-y+2)=0

2x-y-1=0

-x+y-2=0

=x-3=0-->>x=3

30+y=4(3+y)+3

30+y=12+4y+3

30+y=15+4y

15=3y

y=5

number =35

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Answer 2

Answer:

Step-by-step explanation:

Let,  The tens digit ⇒ x and the units digit ⇒ y

2-digit number ⇒ $10x + y$

 

As / per Question,

⇒  $10x + y = 4(x + y) + 3$

⇒  $10x + y = 4x + 4y + 3$

⇒  $6x - 3y = 3$

⇒  $2x - y = 1$   ------- equation 1

And,

⇒  $10x + y + 18 = 10y + x$

⇒  $9x - 9y = -18$

⇒  $x - y = -2$  -------- equation 2

 Subtracting equation 1 from equation 2, We find that,

⇒ $x = 3$  

Putting x value in equation 1   

⇒ $2x - y = 1$

⇒ $2 * 3 - y = 1$  

⇒ $y = 6 - 1$

⇒ $y = 5$  

So, The required number

⇒ $10x + y$

⇒ $10*3 + 5$

⇒ $30 + 5$

⇒ $35$

Therefore,

The required number = 35

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