Question
A number consist of two digits whose sum is five. When the digits are reversed, the number becomes greater by nine. Find the number.
✓
Answer
Let the digits at units and tens place of the given number be x and y respectively. Thus, the number is 10y + x
The sum of the digits of the number is 5. Thus, we have x + y = 5
After interchanging the digits, the number becomes 10x + y
The number obtained by interchanging the digits is greater by 9 from the original number.
Thus, we have
10x + y = 10y + x + 9
⇒ 10x + y - 10y - x = 9
⇒ 9x - 9y = 9
⇒ 9(x - y) = 9
$\Rightarrow\text{x}-\text{y}=\frac{9}{9}$
⇒ x - y = 1
So, we have two equations
x + y = 5
x - y = 1
Here x and y are unknowns. we have to solve the above equations for x and y.
Adding the two equations, we have
(x + y) + (x - y) = 5 + 1
⇒ x + y + x - y = 6
⇒ 2x = 6
$\Rightarrow\text{x}=\frac{6}{2}$
⇒ x = 3
Substituting the value of x in the first equation, we have
3 + y = 5
⇒ y = 5 - 3
⇒ y = 2
Hence, the number is 10 × 2 + 3 = 23
The sum of the digits of the number is 5. Thus, we have x + y = 5
After interchanging the digits, the number becomes 10x + y
The number obtained by interchanging the digits is greater by 9 from the original number.
Thus, we have
10x + y = 10y + x + 9
⇒ 10x + y - 10y - x = 9
⇒ 9x - 9y = 9
⇒ 9(x - y) = 9
$\Rightarrow\text{x}-\text{y}=\frac{9}{9}$
⇒ x - y = 1
So, we have two equations
x + y = 5
x - y = 1
Here x and y are unknowns. we have to solve the above equations for x and y.
Adding the two equations, we have
(x + y) + (x - y) = 5 + 1
⇒ x + y + x - y = 6
⇒ 2x = 6
$\Rightarrow\text{x}=\frac{6}{2}$
⇒ x = 3
Substituting the value of x in the first equation, we have
3 + y = 5
⇒ y = 5 - 3
⇒ y = 2
Hence, the number is 10 × 2 + 3 = 23
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