Question

the sum of a two digit number is 7. if the number formed by reversing the digits is less than the original number by 27,find the original number.
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Answer 1

52

Step-by-step explanation:

Let digit in one's place = 8-x

Digit in tens place = 10x

After reversing, digit in tens place = 10(8-x)

" " " " " , digit in one's place = x

Therefore, B.T.P

=> 10x+7-x -27 = 10[7-x] + x

X = 5

No. = 52

Hope this hepls

Answer 2

Given:

The sum of the digit of a two-digit number is 7. The number formed by reversing the digits is less than the original number by 27.

To find:

The original number.

Solution:

The original number is 52.

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

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

So,

The original number is 10x + y.

Now,

According to the question,

$x + y = 7 \: \: (i)$

Also,

After reversing the digits,

The number becomes 10y + x

So, according to the question,

$10y + x = 10x + y - 27$

This can be written as

$9x - 9y = 27$

$x - y = 3 \: \: (ii)$

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

$2x = 10$

$x = 5$

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

$y = 2$

Now,

Original number = 10x + y = 10(5) + 2 = 52

Hence, the original number is 52.