Question

on reversing the digits of a 2 digit number the number obtained is 9 less than 3 times the original number . difference between the two numbers is 45 find the original number

Answer 1

⭐Answer⭐ :-

The original number is 27 & the reversed number is 72. 

______________________________________

Calculation :-

Let the ones place digit be y & tens place digit be x. 

the original number = 10x+y 

reversed number = 10y+x 

According to question, 

a) 3(10x+y)-9 = 10y+x 

=> 30x+3y-9-10y-x= 0 

=> 29x-7y-9 = 0-----(1) 

b) as the reversed number is bigger, so 

10y+x-(10x+y)=45 

=>10y-y-10x+x-45 = 0 

=> 9y-9x-45=0 

=> y-x-5=0 

=> y= x+5 -----(2) 

now put equation (2) in equation (1) 

29x-7(x+5)-9=0 

=> 29x-7x-35-9=0 

=> 22x=44 

=> x = 2 

Now put the x=2 in equation (2) 

y= 2+5= 7 

Therefore the original number is 27 & the reversed number is 72. 

___________________________________

Answer 2

$\huge{ \underline{ \underline{ \blue{ \sf{ SoLuTiOn :-}}}}}$

Let tens digit place be x and ones digit place be y.

So , the original number = 10x + y

when number is reversed = 10y + x

According to question=>

Case -1

The number obtained is 9 less than 3 times the original number.

=> 3(10x + y) - 9 = 10y + x

=> 30x + 3y - 9 = 10y + x

=> 30x - x + 3y - 10y - 9 = 0

=> 29x - 7y - 9 = 0-------------(1)

Case -2

Difference between two number is 45 and reversed number is greater .

So,

=> 10y + x - (10x + y ) = 45

=> 10y + x - 10x - y = 45

=> 10y - y + x - 10x = 45

=> 9y - 9x = 45

divide by 9 in both sides =>

=> y - x = 5

=> - x = 5 - y

=> x = y - 5--------------(2)

putting x = y - 5 in equ. (1) =>

29x - 7y - 9 = 0

29(y - 5) - 7y - 9 = 0

29y - 145 - 7y - 9 = 0

22y - 154 = 0

22y = 154

y = 154/22

y = 7

putting y = 7 in equ. (2) =>

x = y - 5

x = 7 - 5

x = 2

Here ,

${\purple{\boxed{\large{\bold{x = 2\: and\: y = 7}}}}}$

Therefore, the original number is 27 and reversed number is 72 .