Question

the sum of the digit of a two digit number is 9 if 9 is added to the number formed by reversing the digit then the result is thrice the original number find the original number​​

Answer 1

Answer:

hey I am not sure but this is my solution

let the 2 digit number be 10x+y

therefore 10x + y = 9 equation 1

let the reversed digit be 10y + x

9 + (10x + y) = 3 x (10x + y)

9 + 10x + y = 30x + 3y

9 - 20x = 2y equation 2

-20x + 2y = 9

on using elimination method

-20x + 2y = 9

10x + y = 9

I want to find y first so I am multiplying 2st equation by 2

-20x + 2y = 9

20x + 2y = 18

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

4y = 27/4

in the similar way solve for x and there you go u have ur 2 numbers and then substitute it to the original number 10x+y

hope it helps

Answer 2

Answer :

$\large{\star\:\:\boxed{\bf{The\:Original\:Number\:is\:27\:.}}\:\:\star}$

Explanation :  

Given :–

• Sum of a two digit number is 9 .

• Number obtained by reversing the digits will be 9 more than three times the Original Number.

To Find :–

• The Original Number.

Solution :–

Let the Tens digit of the Original Number be x and the Ones digit be y .

☆ According to the First Condition :-

⇒ x + y = 9  ----------(1)

⇒ 7(x + y = 9)

⇒ 7x + 7y = 63  ---------(2)

☆ According to the Second Condition :-

⇒ 9 + (10y + x) = 3(10x + y)

⇒ 10y + x + 9 = 30x + 3y

⇒ 30x - x + 3y - 10y = 9

⇒ 29x - 7y = 9  -----------(3)

→ Adding Equation(2) and Equation(3) :-

⇒ (7x + 7y) + (29x - 7y) = 63 + 9

⇒ 7x + 29x + 7y - 7y = 72

⇒ 36x = 72

⇒ x = 72/36

⇒ x = 2

→ Putting this Value of 'x' in Equation(1) :-

⇒ 2 + y = 9

⇒ y = 9 - 2

⇒ y = 7

Now we have,

• Tens Digit = 2
• Ones Digit = 7

The number will be = 10(x) + (y) = 10(2) + (7) = 20 + 7 = 27

∴ The number will be 27 .