Question

the sum of digits of a two digit number is 12.If the new number is formed by reversing the digits is greater than the original number by 54 Find the original number​

Answer 1

Answer:

the original no is 30

Step-by-step explanation:

check the answer in the attachment

Answer 2

Answer:

Original number = 39

Step-by-step explanation:

Given that :

• The sum of the digits of a two digit number is 12.
• When the digits are reversed, the new number so formed is greater than the original number by 54.

To find :

• The original number.

Solution :

Let the digit at ten's place be x and the digit at unit's place be y.

★ $\boxed{\bf Original \: Number = 10x + y}$

According to the question,

The sum of the digits of a two digit number is 12.

$\sf \implies x + y = 12 \\\\\implies \sf y = 12 - x \: \: \: \dots (i)$

Also, it is given that ;

When the digits are reversed, the new number so formed is greater than the original number by 54.

Equation :

$\sf \implies 10y + x = 10x + y + 54 \\\\\implies \sf 10y - y - 10x + x = 54 \\\\\implies \sf 9y - 9x = 54\\\\\implies \sf 9(12-x) - 9x = 54 \\\\\implies \sf 108 - 9x - 9x = 54\\\\\implies \sf - 18x = 54 - 108 \\\\\implies \sf - 18x = - 54 \\\\\implies \sf x = \frac{-54}{-18} \\\\\implies \sf x = 3$

Substituting the value of x in (i),

$\sf \implies y = 12 - x\\\\\implies \sf y = 12 - 3\\\\\implies \sf y = 9$

Now, original number = 10x + y

                                    = 10 × 3 + 9

                                    = 30 + 9

                                    = 39

Hence, the required number is 39.