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?


Plz ans this question

Answer 1

Answer:

36 is the number

Step-by-step explanation:

Let the digits be x and y

According to the question,

X+y=9----(1)

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

9y-9x=27-----(2)

Dividing equation (2) by 9,

y-x=3----(3)

(1)+(3)

=2y=12

y=6

y+x=9

X=3

36 is the number

Answer 2

AnswEr:-

Two digit number = 36

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Let the digit at unit's place be m & digit at ten's place be n

∴ Two digit number = 10n + m

Case 1:-

⇒ m + n = 9

⇒ m = 9 - n - - - (Eq.1)

Case 2:-

Interchanging digits we get:-

↠ Two digit number = 10m + n

Therefore,

⇒ 10m + n - (10n + m) = 27

⇒ 10m + n - 10n - m = 27

⇒ 9m - 9n = 27

⇒ 9(m - n) = 27

• Dividing both by 9

⇒ m - n = 3

⇒ m = n + 3 - - - (Eq.2)

Now comparing both equations:-

⇒ 9 - n = n + 3

⇒ - n - n = 3 - 9

⇒ -2n = -6

• Dividing both terms by -2

⇒ n = 3

So,digit at ten's place = 3

Now putting value of n in (Eq.1)

⇒ m = 9 - 3

⇒ m = 6

So,digit at unit's place = 6

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⋆ TWO DIGIT NUMBER:-

⇒ Number = 10n + m

⇒ Number = 10(3) + 6

⇒ Number = 30 + 6

⇒ Number = 36

Therefore,

Two digit number = 36 .

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