Question

Sum of the digits of a two-digit number is 9. When we interchange the digits, it is
found that the resulting new number is greater than the original number by 27. What
is the two-digit number?​

Answer 1

Given,

• Sum of the digits of a two digit number is 9 .
• When we interchange the digits then the resulting new number is greater then the original number by 27.

To Find,

• Two Digit Number

Solution,

⇒Suppose the digit at the ten's place be x

And, Suppose the digit at the one's place be y

Therefore,

• Two Digit number = 10a + b
• Interchange the number = 10b + a

According to the First Condition :-

• Sum of the digits of a two digit number is 9 .

$\implies \sf{x + y = 9}$

$\implies \boxed{\sf{y = 9 - x}}$

According to the Second Condition :-

• When we interchange the digits then the resulting new number is greater then the original number by 27.

$\implies \sf{10x + y + 27 = 10y + x}$

$\implies \sf{10x - x + 27 = 10y - y}$

$\implies \sf{9x + 27 = 9y}$

$\implies \sf{9x - 9y = - 27}$

$\implies \sf{9x -9(9 - x) = -27}$

(Put the value of y From the Equation First )

$\implies \sf{9x -81 + 9x = -27}$

$\implies \sf{18x = 27 + 81}$

$\implies \sf{18x = 54}$

$\implies \sf{x = \dfrac{54}{18}}$

$\implies \boxed{\sf{x = 3}}$

Now Put the value of x in First Condition :-

$\implies \sf{y = 9 - x}$

$\implies \sf{y = 9 - 3}$

$\implies \boxed{\sf{y = 6}}$

Therefore,

$\boxed{\sf{\red{Two \ Digit \ Number = 10x + y = 10(3) + 6 = 36}}}$

$\rule{200}2$

Answer 2

Answer:

$\bullet\large\underline\textsf{The\:two\:digit\:number\:is\:36}$

$\bullet\large\underline\textsf{One's\:place = 3}$

$\bullet\large\underline\textsf{Ten's\:place = 6}$

Step-by-step explanation:

$\large\underline\textsf{Given, }$

Given,

• Sum of two digit number = 9

$\large\underline\textsf{To\:Find, }$

• Two digit number = ?

$\large\underline\textsf{Solution\::}$

↦ Let the unit's digit to be x

↦ Let the ten's digit to be (9 - x)

↦ Now, let the original number :

10(9 - x) + x = 90 - 10x + x = 90 - 9x

↦ On interchanging the digits, the new number is :

10x + (9 - x) = 10x + 9 - x = 9x + 9

☯$\large\underline\textsf{According\:to\:the\:question}$

New number = Original number + 27

⇝ 9x + 9 = 90 - 9x + 27

⇝ 9x + 9 = 117 - 9x

⇝ 9x = 117 - 9 - 9x

⇝ 9x + 9x = 108

⇝ 18x = 108

⇝ x = 108/18

⇝ x = 6

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So, now we will find out our original number/two digit number :

Original number = 90 - (9 × 6) = 90 - 54 = 36

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Know More On :

• https://brainly.in/question/16910451

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