Explanation:

- Let's start with Equation (i): $x^2-7x+t=0$.

- The roots are $p$ and $q$.

- Solving gives: $p+q=7$ and $pq=t$.

- Now, look at Equation (ii): $y^2-4y+(t-9)=0$.

- The roots should be $p$ and $(q-p)$.

- By Vieta's formulas:

- Sum of roots: $p+(q-p)=q=4$

- Product of roots: $p(q-p)=t-9$.

- Using $p+q=7$ and $q=4$, we find $p=3$.

- Substituting $p=3$ back, $pq=t$ becomes: $3\times 4=t$, thus $t=12$.

- Equation (ii) now becomes: $y^2-4y+3=0$.

- Roots are: $y=1$ and $y=3$.

- Multiply Equation (ii) by $2n$:

- Becomes $2n{y}^2-8ny+6n=0$.

- The smallest root is $1$.

- Adding 1 gives: $1+1=2$.

- The resultant number is: 2