Question

The sum of digits of a two digit number is 11. The number obtained by interchanging the digits of the given number exceeds that number by 63. Find the number ​

Answer 1

Answer:

let ones digit be x

let tens digit be y

therefore number

10y +x

ATQ

x+Y=11......1

after interchanging digits

ones place be y

tens place be x

therefore the number is 10 X + Y

equation.

10 X + Y = 10 Y + X + 63

x-y = 7..........2

add 1 and 2

x+y+x-y= 11+7

2x=18

x=9

y = 2

number is 29 or 92

Answer 2

Answer:

$\bigstar{\bold{The\:number=29}}$

Step-by-step explanation:

$\Large{\underline{\underline{\it{Given:}}}}$

• Sum of the digits = 11
• Reversed number = Original number + 63

$\Large{\underline{\underline{\it{To\:Find:}}}}$

• The number

$\Large{\underline{\underline{\it{Solution:}}}}$

→ Let the number in the ten's place be x

→ Let the number in the unit's place be y

→ Hence

  The number = 10x + y

→ By given we know that

  x + y = 11

  x = 11 - y-----(1)

→ Reversing the numbers,

  Reversed numbers = 10y + x

→ By given,

  10y + x = 10x + y + 63

→ Substitute the value of x from equation 1

  10y + 11 - y = 10 (11 - y) + y +  63

  9y + 11 = 110 - 10y + y + 63

  18y = 110 + 63 - 11

  18 y = 162

       y = 162/18

       y = 9

→ Hence the number in the unit's place is 9

→ Substitute the value of y in equation 1

   x = 11 - y

   x = 11 - 9

   x = 2

→ Hence the number in ten's place is 2

→ Therefore the number is 10x + y

   The number = 10 × 2 + 9

   The number = 29

→ Hence the number is 29

$\boxed{\bold{The\:number=29}}$

$\Large{\underline{\underline{\it{Notes:}}}}$

→ A linear equation in two variables can be solved by

• Substitution method
• Elimination method
• Cross multiplication method