The sum of the digits of a 2-digit number is 11. The number obtained b

1.	The sum of the digits of a 2-digit number is 11. The number obtained byinterchanging the digits exceeds the original number by 27. Find the number.
Answer» GivEn: The sum of the digits of a 2-digit number is 11. The number obtained by interchanging the digits exceeds the original number by 27. To find: Find the number. SoluTion: LETS the digit of the number in one's PLACE be x and the number in ten's place be y. Therefore, the number is xy. As per given Question, The sum of the digits of a 2-digit number is 11. $\implies$ x + y = 11 $\implies$ y = 11 - x⠀⠀⠀⠀⠀(1) If one's and ten's place of the number is x and y respectively. Therefore the number is, $\implies$ 10y + x Now, Put the value of x from eq(1) - $\implies$ 10(11 - x) + x $\implies$ 110 - 10x + x $\implies$ 110 - 9x ★ After interchanging, $\implies$ 10x + y $\implies$ 10x + (11 - x) $\implies$ 11 + 9x ━━━━━━━━━━━━━━━ The number obtained by interchanging the digits exceeds the original number by 27. $\implies$ 11 + 9x = 110 - 9x + 27 $\implies$ 11 + 9x = 137 - 9x $\implies$ 9x + 9x = 137 - 11 $\implies$ 18 = 126 $\implies\sf x = \cancel{ \dfrac{126}{18}}$ $\implies$ x = 7 ★ Now, Put the value of x in eq(1) - $\implies$ y = 11 - 7 $\implies$ y = 4 ━━━━━━━━━━━━━━━ ★ Put ths value of x and y in, $\implies$ 10y + x $\implies$ 10 × 4 + 7 $\implies$ 40 + 7 $\implies$ 47 $\therefore$ Hence, the REQUIRED number is 47.

The sum of the digits of a 2-digit number is 11. The number obtained byinterchanging the digits exceeds the original number by 27. Find the number.

Answer»

GivEn:

The sum of the digits of a 2-digit number is 11.

The number obtained by interchanging the digits exceeds the original number by 27.

To find:

Find the number.

SoluTion:

LETS the digit of the number in one's PLACE be x and the number in ten's place be y.

Therefore, the number is xy.

As per given Question,

The sum of the digits of a 2-digit number is 11.

$\implies$ x + y = 11

$\implies$ y = 11 - x⠀⠀⠀⠀⠀(1)

If one's and ten's place of the number is x and y respectively.

Therefore the number is,

$\implies$ 10y + x

Now, Put the value of x from eq(1) -

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

$\implies$ 110 - 10x + x

$\implies$ 110 - 9x

★ After interchanging,

$\implies$ 10x + y

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

$\implies$ 11 + 9x

━━━━━━━━━━━━━━━

The number obtained by interchanging the digits exceeds the original number by 27.

$\implies$ 11 + 9x = 110 - 9x + 27

$\implies$ 11 + 9x = 137 - 9x

$\implies$ 9x + 9x = 137 - 11

$\implies$ 18 = 126

$\implies\sf x = \cancel{ \dfrac{126}{18}}$

$\implies$ x = 7

★ Now, Put the value of x in eq(1) -

$\implies$ y = 11 - 7

$\implies$ y = 4

━━━━━━━━━━━━━━━

★ Put ths value of x and y in,

$\implies$ 10y + x

$\implies$ 10 × 4 + 7

$\implies$ 40 + 7

$\implies$ 47

$\therefore$ Hence, the REQUIRED number is 47.