Question

18) 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.​

Answer 1

Answer:

The number is 35.

Step-by-step explanation:

Since the number is a two-digit number,

We can write the number as 10x + y

x and y are the digits here.

If the digits are exchanged,the new number will be 10y + x.

Sum of digits of the number is 8,so x + y = 8, x = 8-y

10y + x = 10x + y + 18 [Since the new number is increased by 18]

Now we can substitute x = 8-y in the equation we formed,

10 y + (8-y) = 10(8-y) + y + 18

9y + 8 = 80 - 10 y + y + 18

We get,18 y = 90

y= 90/18=5

x = 8- y [ Shown above]

x = 8 - 5

x = 3

So the original number is 10 x + y = 10(3) + 5 = 30 + 5 = 35.

Hope it helps!