Math, asked by Garima1897, 6 hours ago

the sum of digit of a two digit number is 8. The number obtained by interchanging it's digit is 18 more than the original number. Find the original number.​

Answers

Answered by klokeshchandra31
75

Answer:

35

Step-by-step explanation:

x + y =8 -------(1)

10y +x = 18 + 10x + y

y-x = 2 ------(2)

solve equations (1) and (2)

x = 3 and y =5

The original number is 35

Answered by amansharma264
71

EXPLANATION.

Sum of digit of a two digit number is 8.

The number obtained by interchanging it's digit is 18 more than the original number.

As we know that,

Let the one number be = x.

Let other number be = y.

Sum of digit of a two digit number is 8.

⇒ x + y = 8. - - - - - (1).

Let, the original number be = 10x + y.

Let, interchanging number be = 10y + x.

The number obtained by interchanging it's digit is 18 more than the original number.

⇒ 10x + y = 10y + x + 18.

⇒ 10x + y - 10y - x = 18.

⇒ 9x - 9y = 18.

⇒ x - y = 2. - - - - - (2).

From equation (1) & (2), we get.

Adding both the equation, we get.

⇒ x + y = 8. - - - - - (1).

⇒ x - y = 2. - - - - - (2).

We get,

⇒ 2x = 10.

⇒ x = 5.

Put the value of x = 5 in the equation (1), we get.

⇒ x + y = 8.

⇒ 5 + y = 8.

⇒ y = 8 - 5.

⇒ y = 3.

Values of x = 5  and  y = 3.

Original number be = 10x + y.

⇒ 10x + y = 10(5) + 3 = 50 + 3 = 53.

Interchanging number be = 10y + x.

⇒ 10y + x = 10(3) + 5 = 30 + 5 = 35.

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