Question

The sum of the digit of a two digit number is 12 if the new number formed by reserving the digit is greater than the original number by 54 find the original number

Answer 1

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Answer 2

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

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,

$\sf : \implies \: (10y + x) - (10x + y) = 54 \\ \sf : \implies \: 10y + x - 10x - y = 54 \\ \sf : \implies \: 9x - 9y = 54 \\ \sf : \implies \: 9(x - y) = 54 \\ \sf : \implies \: x - y = \frac{54}{9} \\ \sf : \implies \: x - y = 6$

Now we have :

➡ x + y = 12 ...... (i)

➡ x - y = 6 ...... (ii)

Substracting both the equation :

$\sf \: x + y = 12 \\ { \sf{ \underline{x - y = 6}}} \\ \sf : \implies \:2x = 6 \\ \sf : \implies \: x = 3$

After solving we get :

➡ x = 3

Substituting the value of x in equation (i) :

➡ x + y = 12

➡ 3 + y = 12

➡ y = 12 - 3

➡ y = 9

Hence,

The number is :

➡ 10y + x

➡ (10*9) + 3

➡ 93 or, 39 ans.