Question

sum of the digits of a two digit number is 9. when we interchange the digits it is found that the resulting new number is greater than the original number by 27 . what is the two digit number​

Answer 1

Answer:

Step-by-step explanation:

Let the unit digit be y and tens digit be x

Number formed = 10x + y

Reverse number = 10y + x

x + y = 9 (Given)…………………………eq1

10y + x = 10x + y + 27…………………….eq2

9y - 9x = 27

y - x = 3……………………………………..eq3

Solving eq1 and eq3 ,we get

x = 3 and y = 6

Original Number = 36 Reversed Number = 63

You can crosscheck the answer by putting up the values obtained either in eq1 or eq2 or eq 3

Thank You !

OR

Let’s say x is the unit digit and y is the tenth digit.

y+x = 9 -> y=9-x

10x+y = 10y+x+27

10x+9-x = 10(9-x)+x+27

10x+9-x = 90–10x+x+27

18x = 108

x = 6

so y = 3

let’s check

63 - 39 =27

27 = 27 (correct)

Answer 2

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

The Original Number is 36.

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

Given :

Sum of the Digits = 9

The number with interchanged digits is greater than the original number by 27.

To Find :

The Number

Solution :

$\textbf{\small{\underline{Consider the Digits of Original Number as - }}}$

• Units place as x
• Tens place as 10(9 - x)

$\rightarrow$ x + 10(9 - x)

$\rightarrow$ x + 90 - 10x

$\rightarrow$ -9x + 90 ......... [ Original Number ]

$\rule{300}{1.5}$

$\textbf{\small{\underline{The Digits of the Reversed Number -}}}$

• Units Place = (9 - x)
• Tens Place = 10(x)

$\rightarrow$ 9 - x + 10x

$\rightarrow$ 9 + 9x .......... [ Number with Reversed Digits ]

$\rule{300}{1.5}$

$\textbf{\small{\underline{According to the Question - }}}$

The number with interchanged digits is greater than the original number by 27.

★ $\boxed{\tt{9x+9=(-9x+90)+27}}$

$\tt{\longrightarrow} \: 9x + 9 = ( - 9x + 90) + 27$

$\tt{\longrightarrow} \: 9x + 9 = - 9x + 117$

$\tt{\longrightarrow} \: 9x + 9x = 117 - 9$

$\tt{\longrightarrow} \: 18x = 108$

$\tt{\longrightarrow} \: x = \dfrac{108}{18}$

$\tt{\longrightarrow} \: x = 6$

Units Place = 6

$\rule{300}{1.5}$

★ Value of 10(9 - x)

$\tt{\longrightarrow} \:10(9 - 6)$

$\tt{\longrightarrow} \: 10(3)$

$\tt{\longrightarrow} \:30$

$\rule{300}{1.5}$

The Original Number -

$\tt{\longrightarrow} \: 30 + 6$

$\tt{\longrightarrow} \: 36$

$\therefore$ The Original Number is 36.

$\rule{300}{1.5}$

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

Reversed digits of 36 = 63

Check if 63 is more 36 by 27 or not.

$\tt{\longrightarrow} \: 63 - 36$

$\tt{\longrightarrow} \: 27$

$\therefore$ The Original Number is 36.