On dividing a positive integer ‘n’ by 9, we get 7 as a remainder. What will be the remainder, if  $(3\mathrm{n}-1)$ is divided by ‘9’?

Let q be the quotient.
It is given remainder = 7
By Euclid’s algorithm
$\begin{array}{l}\mathrm{n}=3\mathrm{q}+7\\ \Rightarrow 3\mathrm{n}=9\mathrm{q}+21\\ \Rightarrow 3\mathrm{n}-1=9\mathrm{q}+20\\ \Rightarrow 3\mathrm{n}-1=9\times \mathrm{q}+9\times 2+2\\ =9(\mathrm{q}+2)+2\end{array}$

So, when $(3\mathrm{n}-1)$ is divided by 9, we get the remainder = 2