Question

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4. The sum of the digits of a two-digit number is 12. If the digits are reversed, the new number increases by 54.​

Answer 1

Answer:

Step-by-step explanation:

Correct Question :-

The sum of the digits of a two-digit number is 12. If the digits are reversed, the new number increases by 54.​ Find the original number .

Given :-

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

If the digits are reversed, the new number increases by 54.​

To Find :-

The Number

Solution :-

Let the digit in ones place be x

And the digit in tens place be 12 - x

Original Number = 10(12 - x) + 1(x)

= 120 - 10x + x

= 120 - 9x

New Number = 10(x) + 1(12 - x)

= 10x + 12 - x

= 9x + 12

According to the Question,

⇒ New Number - Original Number = 54

⇒  (9x + 12) - (120 - 9x) = 54

⇒ 9x + 12 - 120 + 9x = 54

⇒ 18x - 108 = 54

⇒ 18x = 54 + 108

⇒ 18x = 162

⇒ x = 162/18

⇒ x = 9

Original Number = 120 - 9x = 120 - 81 = 39

New Number = 93

Hence, the numbers are 39 or 93.

Answer 2

$\huge\bold\green{Question}$

The sum of the digits of a two-digit number is 12. If the digits are reversed, the new number increases by 54.

$\huge\bold\green{Answer}$

Let " a " and " b" the digits .So, According to the question :-

→ a + b = 12 ___________________(1)

→ 54 + (10a+b) = (10b+a)

→ 54 + 10a + b = 10b + a

→ 9 a- 9 b = - 54

→ 9 ( a - b) = 54

→ a - b = - 6 ___________________(2)

Now , by adding eqn. (1) and (2) . We get :-

→ a + b + a - b = 12 - 6

→ 2 a = 6

→ a = 3

Hence , we get the value of " a " is 3

Now by substituting this value in eqn (1) we get :-

→ a + b = 12 { a = 3}

→ 3 + b = 12

→ b = 12 - 3

→ b = 9

Hence , we get the value of " b " is 9

Now , we verified it :-

39 + 54 = 93 (verified)

Hence the original no. is 39 and No when digits reversed is 93