What sum of money will amount to Rs. 520 in 5 years and to Rs 568 in 7 years on simple interest?

The correct option is Rs. 400.

To find the principal sum of money, we can use the properties of simple interest. Simple interest earned on a sum of money is constant for every year.

Let the principal sum of money be represented by $P$ and the annual simple interest be represented by $I$.

According to the given information, we have two amounts:

1. The amount after 5 years is Rs. 520:
$P+5I=520$

2. The amount after 7 years is Rs. 568:
$P+7I=568$

By subtracting the amount after 5 years from the amount after 7 years, we obtain the simple interest earned over those 2 years:

Simple interest for 2 years = $568-520=48$

From this, we find the simple interest for 1 year:

Simple interest for 1 year = $\frac{48}{2}=24$

Next, we calculate the interest for 5 years:

Simple interest for 5 years = $5\times 24=120$

Finally, we subtract this 5-year interest from the total amount after 5 years to find the principal sum ($P$):

Principal ($P$) = $520-120=400$

Thus, the sum of money is Rs. 400.