Question

Sum of digits of a two digit number is 8. If their digits are interchanged,
the new number is increased by 18 than the original number. Find the
original number.

give short answer.
​

Answer 1

Let the unit digit be a

let the tens digit be 10

ATO

a +b = 8. Equation i

Original number = 10a + b

Number obtained by interchanging its digits = 10b + a

ATQ

10b + a - 10a + b = 18

9b-9a =19

9 (b-a) =18

b-a = 18 ÷ 9

b - a = 2. Equation ii

On adding equation i and ii

a +b=8

-a+b=2

= 2b = 10

b = 10 ÷2 =5

b = 5

Putting b = 5 in equation i

a +b =8

a +5=8

a =8-5=3

a =3

b = 5

Original number = 10a +b

10 ×3 +5

30+5= 35

Answer 2

Step-by-step explanation:

Let the unit digit be a

let the tens digit be 10

ATO

a +b = 8. Equation i

Original number = 10a + b

Number obtained by interchanging its digits = 10b + a

ATQ

10b + a - 10a + b = 18

9b-9a =19

9 (b-a) =18

b-a = 18 ÷ 9

b - a = 2. Equation ii

On adding equation i and ii

a +b=8

-a+b=2

= 2b = 10

b = 10 ÷2 =5

b = 5

Putting b = 5 in equation i

a +b =8

a +5=8

a =8-5=3

a =3

b = 5

Original number = 10a +b

10 ×3 +5

30+5= 35