Question

Write a two-digit number with sum of its digit is 9?The sum of the two digit number is 9.the number got by interchanging the digit is 27 more than the original number. What is the number number? ​

Answer 1

Correct Question:

The sum of the two-digit number is 9. The number got by interchanging the digit is 27 more than the original number. What is the number? ​

Solution:

Let the number at Tens place be x and number at one's place be y

Tens  |  Ones

  x     |    y

So the original number is 10x + y

The Sum of digits in a 2 digit number is

⇒ x + y = 9        ----- (Equation 1)

Also, The number obtained by interchanging its digits is 27 more than the original number.

10y + x = (10x + y) + 27

⇒ 10y + x - (10x + y) = 27

⇒ 10y + x - 10x - y = 27

⇒ 9y - 9x = 27

⇒ 9(y - x) = 27

⇒ y - x = 27 ÷ 9

⇒ y - x = 3     ----- (Equation 2)

Adding Equations 1 and 2,

          x + y = 9

 (+)    - x + y = 3  

                2y = 12

 ⇒ y = 12 ÷ 2

⇒ y = 6

Substitute value of y in equation 1,

x + y = 9

x + 6 = 9

⇒ x = 9 - 6

⇒ x = 3

We know that the original number is 10x + y

10x + y

= 10(3) + 6

= 36

So, the number is 36

Answer 2

$\mathfrak \red{ANSWER : }$

• Write a two-digit number with sum of its digit is 9?

$\sf \red{a)}36$

• The sum of the two digit number is 9.the number got by interchanging the digit is 27 more than the original number. What is the number number?

• let, the two digits be= xy

• x+y=9

$\tt \: Number \: interchanging= yx$

$\\ \sf \: yx - xy = \red{27} \\ \\ \sf10y + \red{x} - (10 \red{x \: + y}) = 27$

$\sf10y + \red{x} - 10 \red{x \: y} = 27$

$\\ \sf \green{9y - 9x = 27} \\ \sf \: 9(y - x)27 = \\ \sf y - x = \frac{27}{9} = 3$

$\sf \: y + x = 9 \\ \sf y - x = 3$

$\\ \sf \: y = \frac{9 + 3}{2} = \frac{12}{2} = \red 6$

$\\ \sf \: x = \frac{9 - 3}{2} = \frac{6}{2} = \red 3$

$\\ \sf \: x = 3 \\ \sf \: y = 6$

$\tt \: the \: number \: is \: \blue {36}$

$3 + 6 = 9$

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