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the sum of the digits of a two - digit number is 14 . if the digits are reversed, the number increases by 36 . find the number .​

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Avcad0rable

༆ Answer :-

  • 59

༆ Solution :-

Let the tens digit of the number be x .

ones digit = ( 14 - x ) ( since the sum of the 2 digits is 14 )

Two - Digit number = 10 ( tens digit ) + ones digit

Required number ,

  • 10x + ( 14 - x )
  • 10x - x + 14
  • 9x + 14

Reversed number ,

  • 10 ( 14 - x ) + x
  • 140 - 10x + x
  • 140 - 9x

Given ,

Reversed number - Required number = 36

✯ 140 - 9x - ( 9x + 14 ) = 36

✯ 140 - 9x - 9x - 14 = 36

✯ 126 - 18x = 36

✯ 126 - 36 = 18x

✯ 18x = 90

✯ x = 5

  • Ten digits , x = 5
  • Ones digits = ( 14 - x ) = 14 - 5 = 9

♧ Thus , Required number is 10 × 5 + 9 = 59

Given -

  • the sum of the digits of a two - digit number is 14.

i.e, if two numbers are x and y then, x + y = 14

  • if the digits are reversed, the number increases by 36

i.e, if 10y + x then 10y + x = 10x + y + 36.

To find -

  • the number

Concept -

If a, b and c are real number (and if a and b both are not equal to 0) then ax+by=c is called a linear equation in two variables (The two variables are x and y)

The numbers a and b are called the coefficient of the equation ax+by=c. The number r is called the constant of the equation ax+by = c

PS - first we will construct two linear equations and then we'll find the number.

Solution -

Let, x + y = 14

➜ y = 14 - x ----(i)

and we'll solve 10y + x = 10x + y + 36 further,

➜ 10y + x = 10x + y + 36

➜ 10y - y = 10x - x + 36

➜ 9y = 9x + 36

➜ 9x - 9y = -36

➜ 9(x - y) = -36

➜ x - y = -4 ----(ii)

Substituting the value of y (in equation (i)) in equation (ii),

➜ x - (14 - x) = -4

➜ x - 14 + x = -4

➜ 2x = -4 + 14

➜ 2x = 10

➜ x = 10/2

➜ x = 5

Now to find the value of y we will substitute the value of x in equation (i),

➜ y = 14 - 5

➜ y = 9

Therefore, the number is {10(5)+9,i.e,} 59.

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