What sum of money amounts to Rs. $2,600$ in $2$ years and to Rs. $2,700$ in $3$ years at a fixed rate of simple interest annually?

In simple interest, the interest earned every year remains constant.Amount after $3$ years = Rs. $2,700$ Amount after $2$ years = Rs. $2,600$ Interest for $1$ year ($3^{\text{rd}}$ year) = $\text{Amount after 3 years}-\text{Amount after 2 years}$:
$$\text{Interest for 1 year}=2700-2600=\text{Rs. }100$$
Since the interest is uniform every year, the interest accumulated in $2$ years is:
$$\text{Interest for 2 years}=2\times 100=\text{Rs. }200$$
The principal sum ($P$) is the amount after $2$ years minus the interest for $2$ years:
$$P=2600-200=\text{Rs. }2,400$$