Question

the sum of the digits of a 2 digits number is 10. The number obtained by interchanging the digits exceeds the orignal number is 36. find the orignal number. ​

Answer 1

Step-by-step explanation:

Let the units digit of the number be x

And tens digit of the number be y

The original number = 10x + y

The number obtained by interchanging the digits = 10y + x

Case 1:-

The sum of the digits = 10

⇢ x + y = 10......(i)

Case 2:-

Reversed number = Original number + 36

⇢ 10y + x = 10x + y + 36

⇢ 10y + x - 10x - y = 36

⇢ 9y - 9x = 36

Dividing the whole equation by 9

⇢ y - x = 4.......(ii)

Adding equations (i) and (ii)

⇢ x + y + y - x= 10 + 4

⇢ 2y = 14

⇢ y = $\dfrac{14}{2}$ = 7

Substituting y = 7 in equation (i)

⇢ x + y = 10

⇢ x + 7 = 10

⇢ x = 10 - 7 = 3

We have:-

• x = 3

• y = 7

The original number = 10x + y = 10(3) + 7 = 37

∴ The original number = 37