Question

sum of digits of a two digits number is 8 .if their digits are interchanged ,the new number is increased by 18 than the original number. find the original number. (solve this word problem )​

Answer 1

Answer:

The Original Number is 35.

Step-by-step explanation:

Given :

Sum of the digits = 8

The Number with Reversed Digits = 18 more than the original number

To find :

The Original Number

Solution :

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

• Units Place as x
• Tens Place as 10(8 - x)

$\longrightarrow$ 10(8 - x) + x

$\longrightarrow$ 80 - 10x + x

$\longrightarrow$ 80 - 9x ........ [Original Number]

$\rule{300}{1.5}$

Number With Reversed Digits -

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

• Units Place as (8 - x)
• Tens Place as 10(x)

$\longrightarrow$ 10(x) + (8 - x)

$\longrightarrow$ 10x + (8 - x)

$\longrightarrow$ 9x + 8 ....... [Number With Reversed Digits]

$\rule{300}{1.5}$

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

The Number with Reversed Digits = 18 more than the original number

★ $\boxed{\sf{(80 - 9x)+18=9x + 8}}$

$\sf{\longrightarrow} \: (80 - 9x)+18=9x + 8 \\ \\ \sf{\longrightarrow} \: 98 - 9x = 9x + 8 \\ \\ \sf{\longrightarrow} \: 98 - 9 = 9x + 9x \\ \\ \sf{\longrightarrow} \: 90 = 18x \\ \\ \sf{\longrightarrow} \: x = \frac{90}{18} \\ \\ \sf{\longrightarrow} \: x = 5$

$\rule{300}{1.5}$

★ Original Number -

$\sf{\longrightarrow} \: 80 - 9x \\ \sf{\longrightarrow} \: 80 - 9(5) \\ \sf{\longrightarrow} \: 80 - 45 \\ \sf{\longrightarrow} \: 35$

Original Number = 35

$\therefore$ The Original Number is 35.

Answer 2

Answer :-

Original number is 35.

Explanation :-

Let the digit at ten's place be x and the digit at unit's place be y

Given

Sum of the digits = 8

⇒ x + y = 8 --eq(2)

Number formed = 10x + y

Number formed when digits are interchanged = 10y + x

Given

Number formed when digits are interchanged = increased by 18 than the Original number

⇒ 10y + x = 10x + y + 18

⇒ - 18 = 10x + y - 10y - x

⇒ - 18 = 9x - 9y

⇒ - 18 = 9(x - y)

⇒ - 18/9 = x - y

⇒ - 2 = x - y

⇒ x - y = - 2 ---eq(1)

Adding eq(1) and eq(2)

⇒ x + y + (x - y) = 8 + (-2)

⇒ x + y + x - y = 8 - 2

⇒ 2x = 6

⇒ x = 6/2

⇒ x = 3

Substitute x = 3 in x + y = 8

⇒ 3 + y = 8

⇒ y = 8 - 3

⇒ y = 5

Number formed = 10x + y = 10(3) + 5 = 30 + 5 = 35

∴ the original number is 35.