Question

the sum of the digits of a two-digit number is 8 the number obtained by interchanging the two digits exceeds the given number by 18 find the number​

Answer 1

Answer:

Original number = 53

Step-by-step explanation:

given that,

the sum of the digits of a two-digit number is 8

let the digits be x and y

so,

the number will,

10y + x

According to the question,

x + y = 8. ....(1)

now,

also given,

the number obtained by interchanging the two digits exceeds the given number by 18

here,

interchanged digit number = 10x + y

original number = 10y + x

According to the question,

10y + x = 10x + y + 18

10y - y + x - 10x = 18

9y - 9x = 18

9(y - x) = 18

y - x = 18/9

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

now,

we have,

y + x = 8 ..(1)

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

(1) + (2)

y + x + y - x = 8 + 2

2y = 10

y = 10/2

y = 5

putting the value of y on (2)

y - x = 2

5 - x = 2

-x = 2 - 5

-x = -3

x = 3

now,

we have,

x = 3

y = 5

original number =10y + x

putting the values,

10(5) + 3

= 50 +

= 53

so,

Original number = 57