Question

Points 50


sum of the digit of a two digit number is 12. New number formed by reversing the digit is greater than the original by 54. Find the original number.

Solve by both one and two variable.

and plz explain every point of your solution

Answer 1

Answer:

Let the digits be = x and y

x + y = 12 ...(2)

Second equation :-

10y + x = 10x + y + 54

=> 9y - 9x = 54

=> y - x = 6

=> y = 6 + x ... (1)

(1) in (2)

=> x + 6 + x = 12

=> 2x = 6

=> x = 3

y = x + 6 = 9

Number = 39

Answer 2

Answer:

39

Step-by-step explanation:

By 1 variable :-

Given that their sum is 12

Let the number be x.

Let the unit digit be x

and tens digit be 12-x

As we know that any 2 digit number can be written in the form of 10a + b.

So, The original number is :

(x)10 + 12-x

And by reversing it becomes :

(12-x)10 + x

It's given that reversed expression is 54 more than the original.

From this we get an equation -

10x + 12-x = (12-x)10 + x + 54

Solution :-

10x + 12-x = (12-x)10 + x + 54

◌ 9x + 12 = 120 -10x + x + 54

◌18x = 174 - 12

◌x = 162/18

◌ x = 9 (Tens digit)

12 - 9= 3

number = 39

By 2 variables

Given that their sum = 12

x + y = 12

So, the original number =(x )10 + y

by reversing it becomes :

10y + x

It's given in the question that reversed number is 54 more than the original.

so, 10y + x + 54

10x + y + 54 = 10y + x

9x +54 = 9y

9(x + 6) = 9y

x + 6 = y ———eq 1

Now,

we know that x = 12-y

y = 6 + 12 - y

y = 18/2

y = 9

Number = 39