Question

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

Answer 1

Step-by-step explanation:

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Let the given 2 digits as x and y.

so the digits Will be as = 10x + y.

When digits are reversed = 10y + X.

Now,

x +y = 12

y = 12- X.

ACC to the question.

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

10y +x - 10x - y = 18

9y - 9x = 18. (taking 9 common both sides)

y - X = 2

putting the value of y

12-x -x = 2

12-2x = 2

2x = 10

x = 5

y = 12- X = 12-5

y = 7

x = 5

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Answer 2

Let the digits be x and y

Sum of two digit number = 12

x + y = 12

y = 12 - x---(1)

Original number = 10x + y --(2)

New number when the digits are interchanged = 10y + x

Given number formed by interchanging digits exceeds the given numbers by 18.That means given number is 18 more than the new number.

It means the difference between those numbers is 18.

Equation formed :

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

10x + y - 10y - x = 18

9x - 9y = 18

9x - 9(12 - x) = 18 (From (1))

9x - 108 + 9x = 18

18x - 108 = 18

18x = 18 + 108

18x = 126

x = 126/18

x = 7

To know the value of y substitute x = 7 in (1)

y = 12 - 7

y = 5

Substitute x = 7, y = 5 in (2) to know given number

10x + y = 10(7) + 5

= 70 + 5

= 75

Therefore the given number is 75.