Question

The sum of the digits of a 2-digit number is 10. The number obtained by interchanging the digits exceeds the original number by 36. Find the original number.​

Answer 1

Let the -

• ten's digit be M
• one's digit be N

$\therefore$ Number = 10M + N

Sum of two digit number is 10.

=> M + N = 10

=> M = 10 - N ...(1)

The number obtained by interchanging the digits exceeds the original number by 36.

$\therefore$ Interchanged number = 10N + M

=> 10N + M = 10M + N +36

=> 10N - N + M - 10M = 36

=> 9N - 9M = 36

=> N - M = 4

=> N - (10 - N) = 4 [From (1)]

=> N - 10 + N = 4

=> 2N = 14

=> N = 7

Substitute value of N in (1)

=> M = 10 - 7

=> M = 3

•°• Original number = 10M + N

=> 10(3) + 7

=> 30 + 7

=> 37

Answer 2

Answer:

Step-by-step explanation:

let us assume that the two digits are "a" and "b" .

so the number will be= 10a + b

and if interchanged it will be

10b + a

we multiplied the first number because it is on tens place.

according to questions we get two equations.

1. a+b=10
2. 10b+a -{10a+b} =36

     ⇒10b +a -10a -b=36

     ⇒9b -9a =36

⇒9{b-a} = 36

⇒b-a =4

adding two equations which are written in bold we get

 b+a=10

+b-a=4

⇒2b=14

⇒b=7

and by putting the value of "b" in equation 1 we get

⇒a=3

the number will be=10a+b

=10x3+7

=30+7

=37

hope you understood

if any doubt is remaining please contact