Question

The sum of the digits of a two-digit number is 11 if we interchange the digits that the new number formed is 45 less than the original number find the original number

Answer 1

Answer:Two digit number = 83

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

⇒ Original number = m + 10n

Case 1:-

⇒ m + n = 11 [Eq.1]

Case 2:-

★ Interchanged number :-

⇒ New number = n + 10m

According to question:-

⇒ Original number - New number = 45

⇒ m + 10n - (n + 10m) = 45

⇒ m + 10n - n - 10m = 45

⇒ 9n - 9m = 45

⇒ 9(n - m) = 45

⇒ n - m = 45/9

⇒ n - m = 5 [Eq.2]

Now adding both equations:-

So, digit at ten's place = 8

Put this value in (Eq.2)

⇒ 8 - m = 5

⇒ m = 8 - 5

⇒ m = 3

So, digit at unit's place = 3

Now number:-

⇒ Original number = 3 + 10(8)

⇒ Original number = 3 + 80

⇒ Original number = 83

Therefore,

Step-by-step explanation: