Question

one 8 times the sum of its two digit given as that number then number is also obtained by adding two to 13 times the difference of its digits find the number​

Answer 1

Taking the tens place to be x and the units to be y,

the number is then x|y, next to each other.

Equation from the 1st part :

$\sf {10x + y = 8(x+y) + 1}\\\\\\\sf {10x + y = 8x + 8y + 1}\\\\\\\sf {2x - 7y = 1}$

Equation from the 2nd part :

$\sf {10x + y = 13(x-y) + 2}\\\\\\\sf {10x + y = 13x - 13y + 2}\\\\\\\sf {-3x + 14y = 2}$

Now,

$\sf {-3x + 14y = 2}\\\\\\\sf {4x - 14y = 2}$

 

Adding :

$\sf {x = 4}$

 

Substituting into an equation :

$\sf {2 \times 4 - 7y = 1}\\\\\\\sf {8 - 7y = 1}\\\\\\\sf {-7y = -7}\\\\\\\sf {y = 1}$

Required number = 41