Question

the sum of the digits of a 2 digit number is 5. the number formed by reversing the digits is 9 less than the original number. find the original number

Answer 1

AnsWer :

32.

Solution :

Let the tenth place be x

and unit place be y

• Original number Of two digit number be 10x + y.
• Reversing number Of two digit number be 10y + x

Case 1.

The sum of the digits of a 2-digit number is 5.

• X + Y = 5.

$\tt\dagger \: \: \: \: \: \: x + y = 5. \: \: \: \: \: - (1)$

$\rule{90}1$

Case 2.

When The number formed by reversing the digits is 9 less than the original number.

• 10x + y -9 = 10y + x.

$\tt \dagger \: \: \: \: \: 10x + y -9 = 10y + x \: \: \: \: \: - (2)$

$\rule{90}1$

Taking Equation, ( 2 )

$\tt \longmapsto 10x + y - 9 = 10y + x.$

$\tt\longmapsto 10x - x = 10y - y + 9.$

$\tt\longmapsto 9x - 9y = 9.$

$\tt\longmapsto x - y = 1. \: \: \: \: \: - (3)$

$\rule{90}1$

Adding Equation ( 1 ) and ( 3 )

$\begin{tabular}{ c c c c c }x & + & y & = & 5 & \\ x & - & y & = & 1 & \\ \cline{1-5}2x & & & = & 6 & \cline{1-5} \end{tabular}$

$\tt\longmapsto x = \dfrac{6}{2}$

$\tt\longmapsto x = 3.$

Now, Putting the value of x in Equation ( 1 ) We get.

$\tt\longmapsto x + y = 5.$

$\tt\longmapsto 3 + y = 5.$

$\tt\longmapsto y = 5 - 3.$

$\tt\longmapsto y = 2.$

$\rule{90}1$

$\tt \red\bigstar\: Original \: number\begin{cases} \sf{ 10x + y} \\ \sf{ 10(3) + 2 } \\ \sf{ 32 }\end{cases}$

$\tt\red\bigstar\: Reversing \: number\begin{cases} \sf{ 10x + y} \\ \sf{ 10(2) + 3 } \\ \sf{ 23 }\end{cases}$

Therefore, Our Original number become 32.

Answer 2

Question :-

The sum of the digits of a 2 digit number is 5. the number formed by reversing the digits is 9 less than the original number. find the original number..

SoLuTiOn :-

Let the unit digit be x .

Then , the tens digit be 5-x .

Original number = 10(tens digit) + unit digit

= 10(5-x) + x

= 50-10x + x

= 50 - 9x

After interchanging

Unit digit be 5- x

Tens digit be x.

New number = 10 × x + 5 - x

= 9x + 5

According to question

=> 9x + 5 + 9 = 50 - 9x

=> 9x + 14 = 50 - 9x

=> 9x + 9x = 50 - 14

=> 18x = 36

=> x = 2

Unit digit = 2

Tens digit = 5 - 2 = 3

So , Original number = 32