Question

Sum of digit of a two digit number is 8. If 18 is added to the orignal number,the digit interchange their place. Find the two digit.

Answer 1

Answer :

Let the digit at once place be x and ten's place be y.

Original number = 10x + y

If 18 is added,

New number = 10y + x

According to the question :

10x + y + 18 = 10y + x

⇒ 10x - x + y - 10y = - 18

⇒ 9x - 9y = - 18

⇒ 9(x - y) = - 18

⇒ x - y = - 2 .... (i)

And, sum of digits is 8.

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

Adding equation (i) and (ii),

x - y + x + y = - 2 + 8

⇒ 2x = 6

⇒ x = 6/2

⇒ x = 3

Putting the value of x in (ii)

⇒ x + y = 8

⇒ 3 + y = 8

⇒ y = 8 - 3

⇒ y = 5

∴ Required number = 35

Answer 2

Answer:

Step-by-step explanation:

LET THE TWO DIGITS OF THE TWO DIGIT NUMBER BE x and y

by the first condition we can say that

the sum of digit of two digit number is 8

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

now they have given that if we add 18 to the orginal number they would interchange the place

so the orginal number = 10x + y

interchange number  = 10y +x

now by the condition

8 +10x +y = 10y + x

8 = 10y + x - 10x - y

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

now solve (1) and  (2)

x + y =8

-x + y =8

---------------

 2y =16

   y = 8

now sub in 1

so the x = 8 - 8

x =0