Question

Sum of the digits of a two digit number is 9. When 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?


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Answer 1

Step-by-step explanation:

Sum of the digits of a two digit number is 9. When 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 2

Given :

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

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To Find :

• The two-digit number.

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Solution :

Let,

• ones place digit be x.
• tens place digit be y.

So, the two digit number will be : 10y + x.

When we interchange the digits, the two digits number will be 10x + y. And the equation will be : (10x + y) - (10y + x) = 27.

Now, we have two equations :

$\twoheadrightarrow \: \tt{\fbox{x + y = 9}} \: - - - - - - \rm{(Equation \: no. \: 1)}$

$\twoheadrightarrow \: \tt{\fbox{(10x + y) - (10y + x) = 27}} \: - - - - - - \rm{(Equation \: no. \: 2)}$

Let's solve it!!

From equation no. 2, we get

$\mapsto \: \sf{x = \dfrac{27 \: + \: 9y}{9} }$

Substituting the value of x in Equation no. 1, we get

$\sf{ \leadsto \: x + y = 9}$

$\sf{ \leadsto \: \dfrac{27 \: + \: 9y}{9} + y = 9}$

$\sf{ \leadsto \: \dfrac{27 \: + \: 9y \: + \: 9y}{9} = 9}$

$\sf{ \leadsto \: \dfrac{27 \: + \; 18y}{9} = 9}$

$\sf{ \leadsto \: 27 + 18y = 9 × 9 }$

$\sf{ \leadsto \: 18y = 81 - 27}$

$\sf{ \leadsto \: y = \dfrac{ \cancel{54} }{ \cancel{18} } }$

$\sf{ \leadsto \: y = 3}$

Hence, y = 3.

Substituting the value of y in equation no. 2, we get

$\sf{ \Rightarrow \: (10x + y) - (10y + x) = 27 }$

$\sf{ \Rightarrow \: (10x + 3) - (10 × 3 + x) = 27}$

$\sf{ \Rightarrow \: 10x + 3 - 30 - x = 27}$

$\sf{ \Rightarrow \: (10 - 1)x - 27 = 27 }$

$\sf{ \Rightarrow \: 9x = 27 + 27 }$

$\sf{ \Rightarrow \: x = \dfrac{54}{9} }$

$\sf{ \Rightarrow \: x = 6}$

Hence, x = 6.

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The two-digit number is :

ㅤㅤㅤ➺ 10y + x

ㅤㅤㅤ➺ 10(3) + 6

ㅤㅤㅤ➺ 30 + 6

ㅤㅤㅤ➺ 36