Question

The sum of the digits of a two digit number is 12. The number obtained by reversing the digits is 36 greater than the original number. Find the number

Answer 1

Answer:

The Original Number is 48.

Step-by-step explanation:

Given :

Sum of the digits is 12.

The number obtained by reversing the digits is 36 greater than the original number.

To find :

The Original Number

Solution :

$\textsf{\underline{\underline{Original number :-}}}$

Let the digits be -

• Units Place as x
• Tens Place as 10(12 - x)

⇒ 10(12 - x) + x

⇒ 120 - 10x + x

⇒ 120 - 9x .........[Original Number]

$\rule{300}{1.5}$

$\textsf{\underline{\underline{Number with Reversed Digits :- }}}$

Let the digits be -

• Units Place as (12 - x)
• Tens Place as 10(x)

⇒ 10(x) + (12 - x)

⇒ 10x + 12 - x

⇒ 9x + 12 ........[Number With Reversed Digits]

$\rule{300}{1.5}$

$\textsf{\underline{\underline{According to the Question :-}}}$

The number obtained by reversing the digits is 36 greater than the original number.

⇒ 9x + 12 = (120 - 9x) + 36

⇒ 9x + 12 = 156 - 9x

⇒ 9x + 9x = 156 - 12

⇒ 18x = 144

⇒ x = 144/18

⇒ x = 8

$\rule{300}{1.5}$

★ Value of 120 - 9x

⇒ 120 - 9(8)

⇒ 120 - 72

⇒ 48

Original Number = 48

$\therefore$ The Original Number is 48.

Answer 2

Answer:

Step-by-step explanation:

Given :-

The sum of the digits of a two digit number is 12.

The number obtained by reversing the digits is 36 greater than the original number.

To Find :-

The Number

Solution :-

Let the unit digit = x

And the  tens digit = 12 - x

Original number = 10(12 - x) + x

Reversed Number = 10(x) + 12 - x

According to the Question,

⇒ 10(12 - x) + x - 36 = 10x + 12 - x

⇒  120 – 10x + x - 36 = 10x + 12 - x

⇒  -10x + x - 10x + x = 12 – 120 – 36

⇒  -18x = -144

⇒  18x = 144

⇒  x = 144/18

⇒ x = 8x

Unit digit = x = 8

Tens digit = 12 – 8 = 4

The number = 10(4) + 8 = 48

Hence, the Number is 48.