Question

Sum of the two digit number is 9. When we interchange the digits the new number is 27 greater than the earlier number.Find the number.

Answer is 6 how?​

Answer 1

Given :

Sum of the two digit number is 9. When we interchange the digits the new number is 27 greater than the earlier number.

To Find :

The original number.

Solution :

Analysis :

Here we have to form two equations according to the question. Then by solving the linear equations simultaneously we will get our answer.

Explanation :

Let the tens digit be “x” and ones digit be “y”.

According to the question,

• x + y = 9 --------(eq.(i))

Writing the number in expanded form,

• Original number = 10x + y
• Reverse Number = 10y + x

It is said when the digits are interchanged the digits the new number is 27 greater than the earlier number.

☯ According to the question,

⇒ (10y + x) - (10x + y) = 27

Expanding the brackets,

⇒ 10y + x - 10x - y = 27

⇒ 10y - y - 10x + x = 27

⇒ 9y - 9x = 27

Taking 9 as common in LHS,

⇒ 9(y - x) = 27

Dividing both LHS & RHS by 9,

⇒ y - x = 3

∴ y - x = 3 --------(eq.(ii))

From eq.(i) & eq.(ii),

x + y = 9

-x + y = 3

(-) (+) (+)

⇒ 2y = 12

⇒ y = 12/2

⇒ y = 6

∴ y = 6.

• Putting y = 6 in eq(i),

⇒ x + y = 9

⇒ x + 6 = 9

⇒ x = 9 - 6

⇒ x = 3

∴ x = 3.

The number :

• 10x + y = 10 × 3 + 6 = 30 + 6 = 36

The original number is 36.

Answer 2

Answer:

$\huge\green{\boxed{\sf Answer}}$

The sum of the two digits = 9

On interchanging the digits, the resulting new number is greater than the original number by 27.

Let us assume the digit of units place = x

Then the digit of tens place will be = 9–x

Thus the two-digit number is 109–x + x

Let us reverse the digit

the number becomes 10x + 9–x

As per the given condition

10x + 9–x = 109–x + x + 27

⇒ 9x + 9 = 90 – 10x + x + 27

⇒ 9x + 9 = 117 – 9x

On rearranging the terms we get,

⇒ 18x = 108

⇒ x = 6

So the digit in units place = 6

Digit in tens place is

⇒ 9 – x

⇒ 9 – 6

⇒ 3

Hence the number is 36