Question

sum of two digit number is 9.when we interchans the digits, it is found that the result new number is greater then the original number by 27. what is two digit number​

Answer 1

AnswEr :

⠀⠀⠀⌬ Let the Unit's place digit = M

⠀⠀⠀⌬ And the ten's place digit = N

⠀⠀⠀⌬ Then, Original Number = 10(M + N)

⠀⠀⠀⌬ Also, Interchaged Number = 10(N + M)

⠀

• F i r s t⠀C o n d i t i o n :

• Sum of the two digits (M + N) number is 9.

$\twoheadrightarrow\sf M + N = 9 \qquad\quad\qquad\quad\Bigg\lgroup\sf eq^{n}\;(1)\Bigg\rgroup$

• S e c o n d⠀C o n d i t i o n :

⠀

• After Interchanging the digits, the new number is greater than the original number by 27.

⠀

$\longrightarrow\sf (10N + M) - (10M + N) = 27$

$\longrightarrow\sf 9N - 9M = 27$

$\longrightarrow\sf N - M = 3$

$\longrightarrow\sf N = 3 + M \qquad\quad\qquad\quad\Bigg\lgroup\sf eq^{n}\;(2)\Bigg\rgroup$

$\underline{\bigstar\:\sf{Substitue \: the \: value \: of \: N \: from \: eq^n \: (2) \: to \: eq^n \: (1) : }}$

$\longrightarrow\sf M + N = 9$

$\longrightarrow\sf M + 3 + M = 9$

$\longrightarrow\sf 2M = 9 - 3$

$\longrightarrow\sf 2M = 6$

$\longrightarrow\sf M = \cancel\dfrac{6}{2}$

$\longrightarrow\sf M = 3$

$\underline{\bigstar\:\sf{Substituting\;value\;of\;M\;in\;\;eq^n\;(1)\;: }}$

$\longrightarrow\sf M + N = 9$

$\longrightarrow\sf 3 + N = 9$

$\longrightarrow\sf N = 9 - 3$

$\longrightarrow\sf N = 6$

$\underline{\bigstar\:\textsf{Now,\;Original\; Number\; :}}$

$\twoheadrightarrow\sf Original\; Number = 10(M + N)$

$\twoheadrightarrow\sf Original\; Number = 10(3) + 6$

$\twoheadrightarrow\sf Original\; Number = 30 + 6$

$\twoheadrightarrow\underline{\boxed{\pmb{\sf{ Original\; Number =36}}}}$

$\;\;\;\;\;\qquad\therefore{\underline{\textsf{Hence, the Original number is \textbf{36}.}}}$

Answer 2

Given :-

Sum of two digit number is 9.when we interchans the digits, it is found that the result new number is greater then the original number by 27

To Find :-

Number

Solution :-

Let the digit at unit's digit be x.  

Therefore, the digit at ten's place is (9 - x).

Original number = 10(9 - x) + x

Original number = 90 - 10x + x

Original number = 90 - 9x

New number = 10x + (9 - x)

New number = 10x + 9 - x

New number = 9x + 9

ATQ

9x + 9 = (90 - 9x) + 27

9x + 9 = 90 - 9x + 27

9x + 9 = 117 - 9x

9x + 9x = 117 - 9

18x = 108

x = 108/18

x = 6

Therefore

Unit digit = 9 - x = 9 - 6 = 3

Number = 36