Question

A number consists of two digits whose sum is 9. If 9 is subtracted from the number, it's digits are interchanged. Find the number.


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Answer 1

$\huge{\boxed{\bf{\red{Given}}}}$

• A number consists of two digits whose sum is 9.
• If 9 is subtracted from the number, it's digits are interchanged.

$\huge{\boxed{\bf{\purple{To \ Find}}}}$

• Find the number

$\huge{\boxed{\bf{\green{Solution}}}}$

Let,

• the unit digit be y
• ten's digit be x

According to the question

↦ x + y = 9

↦ x = 9 - y _______(1)

↠ (x × 10 + y) - 9 = 10 × y + x

↠ 10x + y - 9 = 10y + x

↠ 10x - x + y - 10y = 9

↠ 9x - 9y = 9 _______(2)

Putting x value in equation (2)

⇒ 9(9 - y) - 9y = 9

⇒ 81 - 9y - 9y = 9

⇒ -18y = 9 - 81

⇒ -18y = -72

⇒ y = $\dfrac{\cancel{72}}{\cancel{18}}$

⇒ y = 4

➙ x = 9-4

➙ x = 5

Now, Finding the number

➵ 10 × x + y

➵ 10 × 5 + 4

➵ 54

✿ Hence, the number is 54

Answer 2

⚽ Given : A number consists of two digits whose sum is 9. If 9 is subtracted from the number, it's digits are interchanged.

$\rule{130}1$

⚽ To Find : the number = ?

$\rule{130}1$

⚽ Solution :

$\begin{lgathered}\bullet\:\:\textsf{Let the unit digit be \textbf{y}}\\\bullet\:\:\textsf{and tens digit be \textbf{x}}\end{lgathered}$

$\underline{ \large \purple{ \mathscr{\dag\:A \bf{ccourding} \: to \: \mathscr {Q} \bf{uestion} :}}}$

$\begin{lgathered}\dashrightarrow\tt\:\:x + y = 9 \\\\\\\dashrightarrow\tt\:\: x = 9 - y \:\:\:\:\bigg\lgroup \textbf{ equation (1)}\bigg\rgroup\\\\\\\dashrightarrow\tt\:\: (x \times 10 + y) - 9 = 10 \times y + x\\\\\\\dashrightarrow\tt\:\: 10x + y - 9 = 10y + x \\\\\\\dashrightarrow\tt\:\: 10x - x + y - 10y = 9\\\\\\\dashrightarrow\tt\:\: 9x - 9y = 9\:\:\:\:\bigg\lgroup \textbf{equation (2)}\bigg\rgroup\end{lgathered}$

$\rule{130}1$

$\underline{\boldsymbol{Putting\: equation \:(1)\: in\: equation\:(2)\:we\:get :}}$

$:\implies\sf 9 (9 - y) - 9y = 2 \\\\\\:\implies\sf 81y - 9y - 9y = 9\\\\\\:\implies\sf - 18y = 9 - 81\\\\\\:\implies\sf - 18y = - 72\\\\\\:\implies\sf y = \dfrac{ - 72}{ - 18}\\\\\\:\implies\sf y = \dfrac{72}{18}\\\\\\:\implies\sf y = 4\\\\\\:\implies\sf x = 9 - 4 \\\\\\:\implies\sf x = 5$

$\rule{130}1$

☯ $\underline{\boldsymbol{The\: Required\:number\:is :}}$

$\begin{lgathered}\longrightarrow\sf 10x + y\\\\\\ \longrightarrow\sf 10(5) + 4\\\\\\ \longrightarrow\sf 50 + 4 \\\\\\ \longrightarrow\underline{\boxed{\sf 54}} \:\:\:\:\bigg\lgroup \bf{Required \:number} \bigg\rgroup\end{lgathered}$

$\therefore\:\underline{\textsf{The required number is \textbf{54}}}.$

$\rule{170}2$