Question

The sum of two digit number is 12.If the new number formed by reserving the digits is greater than the original number by 18. Find the original number.​

Answer 1

Let the digits of the number be x and y

x+y=12 & 10x+y=(10y+x)+54

10x+y-10y-x=54

9x-9y=54

x-y=6

x+y=12

2x=18

x=9

y=12–9=3

Therefore the number is 93 //

93–39=54

Answer 2

${\underbrace{\blue{\textsf{\textbf{Required answer :}}}}}$

Let's assume that the numbers are :

➡ x as ones digit

➡ y as tens digit

Number formed :

➡ 10y + x

Reversing the digits we get :

➡ 10x + y

Now, as it is told that their sum is 12

So,

➡ x + y = 12 .....eq.(i)

According to the question,

$\sf : \implies \: (10y + x) - (10x + y) = 18 \\ \sf : \implies \: 10y + x - 10x - y = 18 \\ \sf : \implies \: 9x - 9y = 18 \\ \sf : \implies \: 9(x - y) = 18 \\ \sf : \implies \: x - y = \frac{18}{9} \\ \sf : \implies \: x - y = 2$

Now we have :

➡ x + y = 12 ...... (i)

➡ x - y = 2 ...... (ii)

Substracting both the equation :

$\sf \: x + y = 12 \\ { \sf{ \underline{x - y = 2}}} \\ \sf : \implies \:2x = 10 \\ \sf : \implies \: x = 5$

After solving we get :

➡ x = 5

Substituting the value of x in equation (i) :

➡ x + y = 12

➡ 5 + y = 12

➡ y = 12 - 5

➡ y = 7

Hence,

The number is :

➡ 10y + x

➡ (10*7) + 5

➡ 75 or, 57