What sum of money will amount to ₹$7,830$ in $6$ years at the rate of $7.5\%$ per annum simple interest?

Let the principal sum of money be $P$.Given:Amount ($A$) = ₹$7,830$ Time ($T$) = $6\text{ years}$ Rate of interest ($R$) = $7.5\%$ per annumThe formula for Simple Interest ($\text{SI}$) is:
$$\text{SI}=\frac{P\times R\times T}{100}$$
The total amount is the sum of the principal and simple interest:
$$A=P+\text{SI}=P+\frac{P\times R\times T}{100}=P\left(1+\frac{R\times T}{100}\right)$$
Substitute the given values into the formula:
$$7830=P\left(1+\frac{7.5\times 6}{100}\right)$$
$$7830=P\left(1+\frac{45}{100}\right)$$
$$7830=P\left(1+0.45\right)$$
$$7830=1.45P$$
Solving for $P$:
$$P=\frac{7830}{1.45}=\frac{783000}{145}=5400$$
Thus, the principal sum of money is ₹$5,400$.