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?

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Answer 1

Answer:

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?

Given :-

• 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.

Find Out :-

• What is the two-digit number?

Solution :-

⊙ Let us assume the digit of units place = x

⊙ Then the digit of tens place will be = (9 – x)

⊙ Thus, the two-digit number is 10(9 – x) + x

⊙ Let us reverse the digit the number becomes 10x + (9 – x)

So, according to the question or ATQ :-

➙ 10x + (9 – x) = 10(9 – x) + x + 27

➙ 9x + 9 = 90 – 10x + x + 27

➙ 9x + 9 = 117 – 9x

On rearranging the terms we get,

➙ 18x = 108

➙ x = $\sf \cancel{\dfrac{108}{18}}$

➙ x = 6

✭ So the digit in units place = 6

✭ Digit in tens place is

➙ 9 – x

➙ 9 – 6

➙ 3

Henceforth, the number is 36

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Answer 2

Given :

• 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.

To Find :

• What is the two-digit number?

Solution :

let,

• Digit at ten's place be x
• Digit at one's place will be 9 - x

Original number :-

$\sf:\implies\: 10x + 9 - x$

$\sf:\implies\: 9x + 9$

New number :-

$\sf:\implies\: 10(90 - x) + x$

$\sf:\implies\: 90 - 10x + x$

$\sf:\implies\red{ 90 - 9x}$

• It is given that the resulting new number is greater than the original number by 27.

According to question :-

$\sf:\implies\: 90 - 9x = 9x + 9 + 27$

$\sf:\implies\: 90 - 9x = 9x + 36$

$\sf:\implies\: 90 - 36 = 9x + 9x$

$\sf:\implies\: 54 = 18x$

$\sf:\implies\: x = 54/18$

$\sf:\implies\red{x = 3 }$

Now ,

• Ten's place digit = x = 3
• One's place digit = 9 - x = 9 - 3 = 6

Number = 36

Hence, the number is 36.