Question

the sum of the digits of a two digit number is 12. If new number formed by reversing the digits is more than the original number by 54. Find the original number​

Answer 1

Answer :

The original number is 39

Given :

• The sum of the digits of a two digit number is 12
• The new number formed by reversing the digits is more than the original number by 54

To Find :

• The original number

Solution :

Let us consider the digits of the two digit number be x and y respectively

Therefore , the number is

$\sf \dashrightarrow 10x + y$

According to question

$\sf \implies x + y = 12........(1)$

Again by question

$\sf \implies 10y + x = 10x + y + 54 \\\\ \sf \implies 10y + x - 10x - y = 54 \\\\ \sf \implies 9y - 9x = 54 \\\\ \sf \implies 9(y - x)=54\\\\ \sf\implies y - x = 6 .........(2)$

Adding (1) and (2) we have

$\sf \implies x + y + y - x = 12+6\\\\ \sf \implies 2y = 18 \\\\ \sf \implies y = 9$

Putting the value of y in (1)

$\sf \implies x + 9 = 12\\\\ \sf \implies x = 12-9\\\\ \sf \implies x = 3$

Thus , the required number is

$\sf \dashrightarrow 10\times3+9 \\\\ \sf \dashrightarrow 39$

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the tens place digit be x.

And the unit's place digit be y.

Number = 10x + y

Reversed number = 10y + x

According to the  Question,

1st part,

⇒ x + y = 12

⇒ y = 12 - x .... (i)

2nd part,

⇒ 10y + x = 10x + y + 54

⇒ 10y - y - 10x + x = 54

⇒ 9y - 9x = 54

⇒ 9(12 - x) - 9x = 54    [From Eq (i)]

⇒ 108 - 9x - 9x = 54

⇒ - 18x = 54 - 108

⇒ - 18x = - 54

⇒ x = 54/18

⇒ x = 3

Putting x's value in Eq (i), we get

⇒ y = 12 - x

⇒ y = 12 - 3

⇒ y = 9

Now, Number = 10x + y = 10(3) + 9 = 39

Hence, the required number is 39.