Question

Sum of the digits or a two-digit number is 9. if we interchange the digits,it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?

Answer 1

GIVEN :

• Sum of the digits or a two-digit number is 9. if we interchange the digits,it is found that the resulting new number is greater than the original number by 27.

TO FIND :

• The two digit number = ?

SOLUTION :

Let the digits at tens place be x and ones place be 9 - x.

The original number = 10x + (9 - x)

➨ 9x + 9

On interchanging the digits, the digits at ones place and tens place will be x and 9 - x respectively.

Therefore, the new number = 10(9 - x)+x

➨ 90 - 10x + x

➨ 90 - 9x

★ According to question :

New number = Original number + 27

➨ 90 - 9x = 9x + 9 + 27

➨ 90 - 9x = 9x + 36

➨ 9x + 9x = 90 - 36

➨ 18x = 54

➨ x = 54/18

➨ x = 3

★ Digit at tens place = 3

★ Digit at one place = 9 - x = 9 - 3 = 6

Therefore, the two digit number is 9x + 9 = 9 × 3 + 9 = 36.

Answer 2

Let the original number be x and y

According to the question :

sum of digits of a two digit number is 9

$\implies \: x + y = 9.....(1)$

Now ,its given :

if we interchange the digits , it is found that the resulting number is greater than the original number by 27 .

The original number be 10x + y

Now, according to the question :

$\implies \: 10y + x - 27= 10x + y$

$\implies \: 10y - y + x - 10x = 27$

$\implies9y - 9x = 27$

$\implies \: 9(y - x) = 27$

$\implies \: y - x = \frac{27}{9} = 3$

$\implies \: y = 3 + x$

Now,

putting the value of y in equation , (1) we get :

➪ x + y = 9

$\implies \: x +( 3 + x )= 9$

$\implies \: x + 3 + x = 9$

$\implies \: 2x + 3 = 9$

$\implies \: 2x = 9 - 3$

$\implies \: 2x = 6$

$\implies \: x = \frac{6}{2} = 3$

So , the value of x is 3

Now , putting the value of x in

equation (1 ) we get :

➪ x + y = 9

➪ 3 + y =9

➪ y = 9 - 3

➪ y = 6

${ \pink{x = 3}}$

${ \orange{y = 6}}$

Therefore , the two digit number is :

➪ 10x + y

➪ 10 × 3 + 6

$\boxed{ \green{36}}$