Question

sum of digits of a 2 digit no. is 8 if the digits are reversed the new number is increased by 10 to twice the original number find the number

Answer 1

Step-by-step explanation:

Let's call the original two digit number xy, where x is the tens digit and y is the ones digit. An algebraic representation of this number is 10x + y.

The sum of the two digit number is 8: x+y=8

When the digits are reversed, the number increases by 36: (10y + x) - (10x + y) = 36

 

Now we have two equations and two unknown parameters, so we have enough information to find those parameters.

 

Solve for x:

X=8-y

 

plug in x:

(10y + 8-y) - (10(8-y)+ y) = 36

 

simplify:

(9y + 8) - (80-9y) = 36

18y - 72 = 36

y = 108/18 = 6

 

so if y=6, then x=8-y=8-6=2

 

so our number is 26. 62 is 36 greater than 26, so everything checks out.

Answer 2

Let x be first digit and y be second, then,

$x + y = 8 \\ 2(10x + y) + 10 = 10y + x \\ x = 8 - y \\ 20(8 - y) + y + 10 = 10y + x \\ 170 - 20y + y = 10y + x \\ 170 - 19y = 10y + 8 - y \\ 170 - 10y = 8 \\ 162 = 10y \\ y = 16.2$