Question

please solve this question

Answer 1

Let the Two Digit Number be : DJ

Given that Sum of the Digits of this Two digit number is 9

⇒ D + J = 9

If we Interchange the Digits the New Two digit number will be : JD

Given that the New Number JD is Greater than DJ by 27

The Difference of New Number JD and Original Number DJ will be 27

⇒ JD - DJ = 27

JD can be Written as 10J + D and DJ can be Written as 10D + J

⇒ 10J + D - (10D + J) = 27

⇒ 10J + D - 10D - J = 27

⇒ 10( J - D) - ( J - D) = 27

⇒ (J - D)(10 - 1) =27

⇒ (J - D) = 27/9 = 3

But we Know that J + D = 9

Adding both J + D = 9 and J - D = 3 we get :

⇒ 2J = 12

⇒ J = 6 and 6 + D = 9 ⇒ D = 3

So the Two Digit Number : DJ is 36