Question

The sum of digits in a two digit number is 9 the number obtained by interchanging digit exceeds the original number by 27. Find the two digit number

Answer 1

Answer:

The original number is 36.

Step-by-step explanation:

Given :

Sum of the digits = 9

Number obtained by interchanging digit exceeds the original number by = 27

To find :

The original number

Solution :

✯ $\textsf{\underline{\underline{Original number -}}}$

• Units place as y
• Tens place as (9 - y)

$\sf{\longrightarrow} \: 10(9 - y) + y \\ \\ \sf{\longrightarrow} \: 90 - 10 + y \\ \\ \sf{\longrightarrow} \: 90 - 9y \:----\rm{\gray{(Original \: Number)}}$

$\rule{300}{1.5}$

✯ $\textsf{\underline{\underline{Number with reversed digits -}}}$

• Units place = (9 - y)
• Tens place = y

$\sf{\longrightarrow} \: 10(y) + 9 - y \\ \\\sf{\longrightarrow} \: 10y + 9 - y \\ \\ \sf{\longrightarrow} \: 9y + 9----\rm{\gray{(Number \: with \: reversed \: digits)}}$

$\rule{300}{1.5}$

✯ $\textsf{\underline{\underline{According to the question - }}}$

Number obtained by interchanging digit exceeds the original number by 27.

$\sf{\longrightarrow} \: 9y + 9 = 90 - 9y + 27 \\ \\ \sf{\longrightarrow} \: 9y + 9 = 117 - 9y \\ \\ \sf{\longrightarrow} \: 9y + 9y = 117 - 9 \\ \\ \sf{\longrightarrow} \: 18y = 108 \\ \\ \sf{\longrightarrow} \: y = \dfrac{108}{18} \\ \\ \sf{\longrightarrow} \: y = 6$

$\rule{300}{1.5}$

✯ $\textsf{\underline{\underline{Original Number - }}}$

$\sf{\longrightarrow} \: 90 - 9y \\ \\ \sf{\longrightarrow} \: 90 - 9(6) \\ \\ \sf{\longrightarrow} \: 90 - 54 \\ \\ \sf{\longrightarrow} \: 36$

Orignal number = 36

$\therefore$ The original number is 36.

Answer 2

||✪✪ QUESTION ✪✪||

The sum of digits in a two digit number is 9 the number obtained by interchanging digit exceeds the original number by 27. Find the two digit number

|| ✰✰ ANSWER ✰✰ ||

Let The Original Number be (10x + y) . where as (x + y) is 9 .

→ After interchanging The Digits = (10y+x) .

So,

→ x + y = 9 ------------- Equation ❶

And,

→ (10y+x) - (10x +y) = 27

→ 10y + x - 10x - y = 27

→ 9y - 9x = 27

→ 9(y - x) = 27

Dividing both sides by 9,

→ (y - x) = 3 ----------- Equation ❷

Adding Equation ❶ & ❷ Now, we get,

☛ (x + y) + (y - x) = 9 + 3

☛ 2y = 12

Dividing both sides by 2 ,

☛ y = 6

Putting The value in Equation ❶ Now,

☛ x + 6 = 9

☛ x = 9-6

☛ x = 3

Hence, The Required Two - Digit Number = 10x + y = 10*3 + 6 = 36 (Ans).