Question

the sum of two digit number is 11. if you subtract 27 from the number the digits are reversed . what is the number​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The Number is 74

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Sum of the Digits of the Number = 11

If 27 is subtracted from the number the digits are reversed.

To Find :

The Numbers

Solution :

$\textbf{\small{\underline{Consider the Digits of Original number as -}}}$

• Units Place = x
• Tens Place = 10(11 - x)

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

$\longrightarrow$ 10(11 - x) + x

$\longrightarrow$ 110 - 10x + x

$\longrightarrow$ 110 - 9x ..... [ Original Number ]

$\rule{300}{1.5}$

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

If 27 is subtracted from the number the digits are reversed.

◆ $\textbf{\small{\underline{The Reversed Digits of the Number -}}}$

• Units Place = 11 - x
• Tens Place = 10(x)

$\rule{300}{1.5}$

★ $\boxed{\sf{(110-9x)-27=10x+11-x}}$

$\longrightarrow$ (110 - 9x) - 27 = 10x + 11 - x

$\longrightarrow$ 110 - 27 - 9x = 10x - x + 11

$\longrightarrow$ 83 - 9x = 9x + 11

$\longrightarrow$ -9x - 9x = 11 - 83

$\longrightarrow$ -18x = -72

$\longrightarrow$ 18x = 72

$\longrightarrow$ x = 72/18

$\longrightarrow$ x = 4

Units Place = 4

$\rule{300}{1.5}$

★ Value of 10(11 - x)

$\longrightarrow$ 10(11 - 4)

$\longrightarrow$ 10(7)

$\longrightarrow$ 70

Tens = 70

$\rule{300}{1.5}$

◆ $\textbf{\small{\underline{The Number -}}}$

• Units Place = 4
• Tens = 70

Number = 70 + 4 = 74

$\therefore$ The Number is 74

$\rule{300}{1.5}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

Subtract 27 from 74

$\longrightarrow$ 74 - 27

$\longrightarrow$ 47

47 has reversed digits of 74.

$\therefore$ The Number is 74

Answer 2

Answer :-

The number is 74

Solution :-

Let the two digits of a two digit number be x and y

Sum of two digits of a two digit number = 11

x + y = 11

y = 11 - x ---- (1)

Original number = 10(x) + y = 10x + (11 - x) = 10x + 11 - x = 9x + 11

Number when digits are reversed = 10(y) + x = 10(11 - x) + x = 110 - 10x + x = 110 - 9x

Given

Original number - 27 = Number when digits are reversed

(9x + 11) - 27 = 110 - 9x

9x + 11 - 27 = 110 - 9x

9x - 16 = 110 - 9x

9x + 9x = 110 + 16

18x = 126

x = 126/18

x = 7

Therefore Ten's place = 7

Substitute x = 7 in (1)

y = 11 - x

y = 11 - 7

y = 4

Now to find the number substitute value of x in 9x + 11

9x + 11

= 9(7) + 11

= 63 + 11

= 74

Therefore the number is 74.