Question

In a two digit number sum of it's digits is 12. If the digits are interchanged, the difference between the new and the original number is 54. Find the two digit number.​

Answer 1

Answer:

The two digit number is 39

Step-by-step explanation:

Let,

Units digit = x

Tens digit = 12 - x

The sum of 2 digit = 12

Original number :

⇒ 10 (12 - x) + x

⇒ 120 - 10x + x

⇒ 120 - 9x

The digits are interchanged

⇒ 10x + (12 - X)

⇒ 10x - x + 12

⇒ 9x + 12

The new number is 54 more than the original

⇒ (120 - 9x) + 54 = 9x + 12

⇒ 120 + 54 - 9x = 9x + 12

⇒ 174 - 9x = 9x + 12

⇒ - 9x - 9x = 12 - 174

⇒ - 18x = - 162

⇒ 18x = 162

⇒ x = 162 / 18

⇒ x = 9

★ Units digit = 9

Tens digit = 12 - x

⇒ 12 - 9

⇒ 3

★ Tens digit = 3

Therefore,

The two digit number is 39

Answer 2

$\bf\huge{ANSWER}$

Let the digit in tens place be x and the digit in ones place be y .

Original number = 10x + y

New number = 10y + x

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→ According to the first condition ,

$\rm\longrightarrow x+y = 12 \ \ \ \ \ \ \ \ ..........(1)$

→ According to the second condition ,

$\rm\longrightarrow (10y+x)-(10x+y)=54\\\\\longrightarrow 10y+x-10x-y=54\\\\\longrightarrow 9y-9x=54\\\\\longrightarrow 9x-9y=-54\\\\\longrightarrow x-y=-6 \ \ \ \ \ \ \ \ \ ...........(2)$

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Add Eq (1) and Eq (2) ,

$\longrightarrow \rm 2x=6\\\\\longrightarrow\bf x=3$

Put the value of x in Eq (1)

$\rm\longrightarrow 3+y=12\\\\\longrightarrow\bf y=9$

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The two digit number is 39 .