Question

the sum of digits of a two digits number is 9.the number obtained by reversing the order of digits is 45more than the original number. find original number?​

Answer 1

Answer:

The Original Number is 27.

Step-by-step explanation:

Given :

Sum of the two digits of a number = 9

Number obtained by reversing = 45 more than the original number

To find :

The Original Number

Solution :

Original Number -

Let the digits be - $\textbf{\small{\underline{}}}$

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

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

$\longrightarrow$ 90 - 10x + x

$\longrightarrow$ 90 - 9x ......... [Original Number]

$\rule{300}{1.5}$

Number with Reversed Digits -

Let the digits be - $\textbf{\small{\underline{}}}$

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

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

$\longrightarrow$ 10x + 9 - x

$\longrightarrow$ 9x + 9 .......... [Number With Reversed Digits]

$\rule{300}{1.5}$

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

Number obtained by reversing = 45 more than the original number

★ $\boxed{\sf{(90-9x)+45=9x+9}}$

$\sf{\longrightarrow} \: (90-9x)+45=9x+9 \\ \\ \sf{\longrightarrow} \:135 - 9x = 9x + 9 \\ \\ \sf{\longrightarrow} \:135 - 9 = 9x + 9x \\ \\ \sf{\longrightarrow} \:126 = 18x \\ \\ \sf{\longrightarrow} \:x = \dfrac{126}{18} \\ \\ \sf{\longrightarrow} \:x = 7$

$\rule{300}{1.5}$

$\textbf{\small{\underline{Original Number - }}}$

$\sf{\longrightarrow} \:90 - 9(7) \\ \sf{\longrightarrow} \:90 - 63 \\ \sf{\longrightarrow} \:27$

$\therefore$ The Original Number is 27.

Answer 2

Answer :-

Original number is 27.

Explanation :-

Let the digit at tens place be x and digit at units place be y

Sum of digits = 9

⇒ x + y = 9 --eq(1)

Number formed i.e original number = 10x + y

Number obtained when digits are reversed = 10y + x

Given

Number obtained when digits are reversed = 45 more than the original number

⇒ 10y + x = 10x + y + 45

⇒ - 45 = 10x + y - 10y - x

⇒ - 45 = 9x - 9y

⇒ - 45 = 9(x - y)

⇒ - 45/9 = x - y

⇒ - 5 = x - y

⇒ x - y = - 5 --eq(2)

Adding eq(1) and eq(2)

⇒ x + y + (x - y) = 9 + (-5)

⇒ x + y + x - y = 9 - 5

⇒ 2x = 4

⇒ x = 4/2

⇒ x = 2

Substitute x = 2 in x + y = 9

⇒ 2 + y = 9

⇒ y = 9 - 2

⇒ y = 7

Original number = 10x + y = 10(2) + 7 = 20 + 7 = 27.

∴ the original number is 27.