Question

sum of the digits of a two digits of a two digit number is 12. the given number exceeds the number obtained interchanging the digits by 36 . find the given number​

Answer 1

Answer:

84

Step-by-step explanation:

Let one's digit be x.

Then, ten's digit =12−x

Number =10(12−x)+x=120−10x+x=120−9x

Number obtained by reversing the digits =10(x)+12−x=12+9x

According to the given condition, we have

120−9x=12+9x+36

⇒120−12−36=9x+9x

⇒72=18x

⇒x=4

So, the number =120−9x=120−9×4=120−36=84

Hence, the required number is 84

Answer 2

> the number is either 48 or 84

Question:

sum of the digits of a two digits of a two digit number is 12. the given number exceeds the number obtained interchanging the digits by 36 . find the given number

Solution:

x+y = 12_____(1) [•°• sum of the digits of a two digits of a two digit number is 12.]

10x+y=10y+x - 36 [•°• number exceeds the number obtained interchanging the digits by 36 .]

= 10x - x + y - 10y = - 36

= 9x - 9y = - 36

= 9(x - y) = - 36

x - y = -4_____(2)

Subtracting eqn(2) from eqn(1):

= x - y - (x + y) = -4 - 12

= x - y - x - y = -16

= - 2y = -16

= y = 8

putting the value of y in eqn(1):

x+y= 12

= x + 8 = 12

= x = 12 - 8

= x = 4

Hence, x = 4 and y = 8

so, the number is either 48 or 84