Question

3. 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 1

Answer:

The Original Number is 36.

Step-by-step explanation:

Given :

Sum of the Digits = 9

The number with interchanged digits is greater than the original number by 27.

To Find :

The Number

Solution :

Orignal Number,

• Units place as x
• Tens place as 10(9 - x)

⇒x + 10(9 - x)

⇒ x + 90 - 10x

⇒ -9x + 90 ......... [ Original Number ]

Number with reversed digits,

• Units Place = (9 - x)
• Tens Place = 10(x)

⇒ 9 - x + 10x

⇒ 9 + 9x .......... [ Number with Reversed Digits ]

The number with interchanged digits is greater than the original number by 27.

⇒ 9x + 9 = ( –9x + 90) + 27

⇒ 9x + 9 = - 9x + 117

⇒ 9x + 9x = 117 - 9

⇒ 18x = 108[

⇒ x = 108/18

⇒ x = 6

Units Place = 6

★ Value of 10(9 - x)

⇒ 10(9 - 6)

⇒ 10(3)

⇒ 30

The Original Number -

⇒ 30 + 6

⇒ 36

The Original Number is 36

Answer 2

Answer:-

Let the number be (10x + y).

Given:

Sum of the digits = 9.

→ x + y = 9

→ x = 9 - y -- equation (1).

And,

When we interchange the digits, the resulting number is greater than the original number by 27.

That is,

(10x + y) + 27 = 10y + x

Substitute "x" value here,

→ 10(9 - y) + y + 27 = 10y + 9 - y.

→ 90 - 10y + y + 27 = 9y + 9.

→ 117 - 9 = 9y + 9y

→ 18y = 108

→ y = 108/18

→ y = 6

Substitute "y = 6" in equation (1).

→ x = 9 - y

→ x = 9 - 6

→ x = 3

Two - digit number = 10(3) + 6 = 36

Therefore, the number is 36.