Question

The sum of the digits of a two digit number is 12. The number obtained by interchanging the two digits exceeds the given number by 18. Find the number.

Answer 1

x+y=12......(i)

18+(10x+y)=10y+x

9x-9y=-18

x-y=-2.........(ii)

solving i and ii

x+y=12

x-y=-2

________

2x=10

x=5

so y=7

Answer 2

Answer : 57.

Step-by-step explanation:

Given :

The sum of the digits of a two digit number is 12. The number obtained by interchanging the two digits exceeds the given number by 18.

To Find :-

The number.

Let the numbers are x and y.

Two-digit number is = 10x + y

The reversed number = 10y + x

Given:

x + y = 12

y = 12 – x -----------1

Also, it is given:

10y + x - 10x – y = 18

9y – 9x = 18

y – x = 2 -------------2

Substitute the value of y from eqation 1 in eqn 2

12 – x – x = 2

12 – 2x = 2

2x = 10

x = 5

Finding the value of y :-

y = 12 – x

=> 12 – 5 = 7

=> y = 7.

X = 5 and y = 7.

Hence, the two-digit number is :-

10x + y

=> (10*5) + 7 = 57

The two digit number is 57