Question

The sum the digits of a two digit number is 7 if the digits are reversed. The number formed is 9 less than the original no. find the no.

Answer 1

Hi there !!
Here's your answer

Let the digit in the units place be x
The sum of digits of the number is 7

digit in tens place = 7 - x
The original number formed will be
10(7-x) + x
= 70 - 10x + x
= 70 - 9x ______(i)

Given,
if the digits are reversed,The number formed is 9 less than the original Number

So,
after interchanging the digits,
we have,
digit in units place = 7 - x
Digit in tens place = x
The new number formed will be
10(x) + 7 - x
= 10x + 7 - x
= 9x + 7 _______(ii)

Since the new number formed is 9 less than the original number, the following balanced equation will be formed


$70 - 9x - 9 = 9x + 7$

$61 - 9x = 9x + 7$

Transposing the terms ,
we have,

$61 - 7 = 9x + 9x$

$54 = 18x$

$x = \frac{54}{18}$
x = 3

Therefore,
the digit in units place = x = 3
digit in tens place = 7 - x = 7-3 = 4

Thus,
the original number is 43

Answer 2

☆Hey Mate!!!☆

Let the original number be 10x + y,

Equation :-

10y + x = 10x + y - 9

9 = 10x + y - 10y - x

9 = 9x - 9y

Each getting 1,

x - y = 1 _______(1)

x + y = 7 _______(2)

Adding both equations,

2x = 8, x = 8/2 => x = 4

Putting 4 in (1) equation

4 - y = 1

4 - 1 = y

3 = y

So, original number is 43 and reversed number is 34.

Hope it helps☺!