Explanation:

Let the principal amount be $P$. The formula for Amount ($A$) in simple interest is $A = P + \text{SI}$, where $\text{SI}$ is the simple interest. \nGiven information: 1. Amount after $2$ years ($A_2$) = $₹704$. 2. Amount after $5$ years ($A_5$) = $₹800$. \nSince it's simple interest, the interest earned each year is constant. The difference in the amounts is solely due to the interest accumulated over the additional years.\nInterest earned in $(5 - 2) = 3$ years $= A_5 - A_2 = ₹800 - ₹704 = ₹96$. \nNow, we can find the simple interest earned per year:\nSimple Interest for $1$ year $= \frac{₹96}{3 \text{ years}} = ₹32$. \nNext, calculate the simple interest earned in $2$ years:\nSimple Interest for $2$ years $= 2 \times ₹32 = ₹64$. \nWe know that $A_2 = P + \text{Simple Interest for } 2 \text{ years}$.\nSubstitute the values: $₹704 = P + ₹64$.\nTo find the principal $P$: $P = ₹704 - ₹64 = ₹640$. \nLet's evaluate the options:\nOption (1) $₹600$: If $P=₹600$, then $\text{SI}_2 = ₹704 - ₹600 = ₹104$. This implies annual interest of $₹52$, which contradicts the calculated $₹32$.\nOption (2) $₹640$: This matches our calculated principal. If $P=₹640$, then $\text{SI}_2 = ₹704 - ₹640 = ₹64$, which is $2 \times ₹32$. This is consistent.\nOption (3) $₹660$: If $P=₹660$, then $\text{SI}_2 = ₹704 - ₹660 = ₹44$. This implies annual interest of $₹22$, which contradicts $₹32$.\nOption (4) $₹680$: If $P=₹680$, then $\text{SI}_2 = ₹704 - ₹680 = ₹24$. This implies annual interest of $₹12$, which contradicts $₹32$. \nTherefore, the principal amount is $₹640$. The correct option is (2) ₹640.