Question

the sum of the digit of the two digit number is 7 the number formed by reversing the digit digits is 45 more than the original number find the original number​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The Original Number is 61.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

$\text{\underline{\underline{\purple{Given :}}}}$

Sum of the two digits of the number = 7

The number formed by reversing the digits is : 45 more than the original number find the original number.

$\text{\underline{\underline{\purple{To Find :}}}}$

The number

$\text{\underline{\underline{\purple{Solution :}}}}$

In the Original Number ;

Consider the digit at -

• Units place as x
• Tens place as 10(7 - x)

Original Number = 10(7 - x) + x

$\tt{\longrightarrow}$ 70 - 10x + x

$\tt{\longrightarrow}$ 70 - 9x ...........[ 1 ]

Number after reversing the digits ;

• Tens Place will be 10(x)
• Units Place will be (7 - x)

Reversed Number = 10x + 7 - x

$\tt{\longrightarrow}$ 9x + 7 ...........[ 2 ]

$\rule{300}{1.5}$

As Given in the Question ;

The Number obtained by reversing the digits is 45 more than the original number.

• Original Number = 70 - 9x
• Reversed Number = 9x + 7

★ $\boxed{\sf{70-9x=(9x+7)+45}}$

$\tt{\longrightarrow} \: 70 - 9x = 9x + 7 + 45$

$\tt{\longrightarrow} \: 70 - 9x = 9x +52$

$\tt{\longrightarrow} \: 70 - 52 = 9x + 9x$

$\tt{\longrightarrow} \: 18x = 18$

$\tt{\longrightarrow} \: x = \dfrac{18}{18}$

$\tt{\longrightarrow} \: x =1$

The Units place is 1

$\rule{300}{1.5}$

★ Value of 10(7 - x)

$\tt{\longrightarrow} \: 10(7 - 1)$

$\tt{\longrightarrow} \: 70 - 10$

$\tt{\longrightarrow} \: 60$

$\rule{300}{1.5}$

The Number =

$\tt{\longrightarrow} \: 60 + 1$

$\tt{\longrightarrow} \: 61$

$\therefore$ The Original Number is 61.

$\rule{300}{1.5}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

The Original Number is 61 and Reversed Number is 16. If their difference is 45, then the answer is Correct.

$\tt{\longrightarrow} \: 61 - 16 = 45$

$\tt{\longrightarrow} \: 45 = 45$

$\therefore$ The Original Number is 61.

Answer 2

Let the ones digit = x

Then the tens digit = 7-x

The number = (7-x)10+x

According to question,

x*10+(7-x) = (7-x)10+x+45

10x+7-x = 70-10x+x+45

9x+7 = 115-9x

18x = 108

x = 108/18 = 6

So , the original number = (7-x)10+x

= (7-6)10+6

= 16

And the reversed number = 61

So , the original number so required = 16.

The above method used is from the topic - "Linear Equations in one variable".