Question

The difference between a 2-digit number and the number obtained by interchanging its
digits is 27. What is the difference between the sum and the difference of the digits of the
ber if the ratio between the digits of the number is 1:2?​

Answer 1

Solution :

Required difference = 6

Step by step Explanation

Let the unit digit of a number be y and ten's place be x , then

• Number = 10x+y
• Number obtained on interchanging = 10y+x

According to the Question

Difference between a 2-digit number and the number obtained by interchanging it digits is 27.

Difference= 27

$\sf\implies27=(10x+y)-(10y+x)$

$\sf\implies27= 9x-9y$

$\sf\implies9(x-y)=27$

$\sf\implies\:x-y=3$

Given : The ratio between the digits of the no is 1:2

Thus ,

Possible combinations are (2,5) (3,6) (4,7) (5,8) (6,9)

Thus , Possible combination is (3,6)

Sum of digits = 6+3 = 9

Diffence of digits = 6-3 = 3

Therefore, the difference between the sum and the difference of the digits of the no is 9-3 = 6 .

Answer 2

$Given :-$

• The difference between a two digits number and the number obtained by interchanging it's digits is 27 .
• The ratio between the digits of the number is 1:2.

$Find\: Out :-$

• What is the difference between the sum and the digits.

$Solution :-$

Let, unit digits be x and tenth digits be y

So, the original number will be 10x + y

And, their interchanging number will be 10y + x

The difference between the two numbers is 27.

According to the question,

↪ (10x + y) - (10y + x) = 27

↪ 10x + y - 10y - x = 27

↪ 10x - x -10y + y = 27

↪ 9x - 9y = 27

↪ 9(x - y) = 27

↪ x - y = $\sf\dfrac{\cancel{27}}{\cancel{9}}$

➤ x - y = 3

Now, given ratio is 1:2,

↪ $\dfrac{y}{x}$ = $\dfrac{1}{2}$

➙ x = 2y

By putting the value, we get,

⇒ x - y = 3

⇒ 2y - y = 3

⇒ y = 3

Hence, x = 2(3) = 6

Since, the sum of their digits will be,

↪ x + y

↪ 6 + 3

↪ 9

And, their differences is,

↪ x - y

↪ 6 - 3

↪ 3

$\therefore$ The difference between the sum and the difference of digits of the number is 9 - 3 = 6.