Question

The sum of the digits of a two number is 5. On reversing the digits of the number, it exceeds the original number by 9. Find the
original number.

Answer 1

Solution :

Let the number in the tenth place be x and the number in the one's place be y.

Then, according to the question

x + y = 5

x = 5 - y

The original number is in the form ;

10x + y

On reversing the digits of the number, it exceeds the original number by 9,then the equation becomes ;

Reversed number - original number = 9

10y + x - (10x +y) = 9

10y + x - 10x - y = 9

9y - 9x = 9

y - x = 1

Substituting the value of x = 5 - y, we get

y - ( 5-y) = 1

y - 5 + y = 1

2y - 5 = 1

2y = 1+5

y = 6/2 = 3

And, x = 5 - y = 5 - 3 = 2.

Hence, the number is 23.

Answer 2

$\huge\sf\pink{Answer}$

☞ Original Number = 23

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ The sum of the digits of a two digit number = 5

✭ When they are reversed the new number exceeds the original number by 9

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

☆ The original number?

$\rule{110}1$

$\huge\sf\purple{Steps}$

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

Original number = 10x + y

According to the question ;

➝ 10x + y + 9 = 10y + x

➝ 10x - x + y - 10y = - 9

➝ 9x - 9y = - 9

➝ 9(x - y) = - 9

➝ x - y = $\sf \dfrac{-9}{9}$

➝ x - y = - 1.... (i)

$\rule{110}1$

❍ Also, it is given that the sum of the digits of the two digit number is 5.

➳ x + y = 5.... (ii)

On adding equation (i) and (ii)

➳ x - y + x + y = 5 - 1

➳ 2x = 4

➳ x = $\sf \dfrac{4}{2}$

➳ x = 2

Putting the value of x in (i)

➢ x - y = - 1

➢ 2 - y = - 1

➢ y = 2 + 1

➢ y = 3

$\rule{110}1$

✪ Original number = 10x + y

$\twoheadrightarrow\sf 10 × 2 + 3$

$\twoheadrightarrow\sf 20 + 3$

$\orange{\twoheadrightarrow\sf Original\: Number = 23}$

$\rule{170}3$