Question

a two digit no is obtained by either multiplying sum of digits by 8 and adding 1 or by multiplying the difference of the digits by 13 and adding 2.Find the no.

Answer 1

Hi,

Let's assume a and b the 2 digits:

$\overline{ab}=10*a+b=(a+b)*8+1\ \Rightarrow\ 2a-7b=1\ (1)\\\\ \overline{ab}=10*a+b=(a-b)*13+2\ \Rightarrow\ 3a-14b=-2\ (2)\\\\ (1)-2*(2)\ \Rightarrow\ -a=-4\ \Rightarrow\ a=4\\ (1)\ \Rightarrow\ b=\dfrac{8-1}{7}=1$

The number is 41.