Question

the sum of the digit of two digit number is 10 .the number obtained by interchanging the digits exceeds the original number by 36. find the original number.

Answer 1

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Answer 2

Given:

The sum of the digit of a two-digit number is 10. the number obtained by interchanging the digits exceeds the original number by 36.

To find:

The original number.

Solution:

The original number is 37.

To answer this question, we will follow the following steps:

Let the digits of a two-digit number be xy where x is at ten's place while y is at one's place.

The original number is 10x + y.

So,

According to the question,

$x + y = 10 \: \: \: (i)$

Also,

After interchanging the digits,

The number becomes 10y + x

So, according to the question,

$10x + y + 36 = 10y + x$

$9y - 9x = 36$

$y - x = 4 \: \: (ii)$

After adding (i) and (ii), we get,

$2y = 14$

$y = 7$

On putting the value of y in (i), we get

$x = 3$

Now,

Original number = 10x + y = 10(3) + 7 = 37

Hence, the original number is 37.