To determine the rate percent at which the interest on Rs. 6300 in 10 years will be equal to the principal, we can follow these steps:
1. Understand the given information:
- Principal (P) = Rs. 6300
- Time (T) = 10 years
- Interest (I) = Principal (since the interest is equal to the principal)
2. Recall the formula for simple interest:
[tex]\[
\text{Simple Interest} (SI) = \frac{P \times R \times T}{100}
\][/tex]
where [tex]\( P \)[/tex] is the principal, [tex]\( R \)[/tex] is the rate of interest per annum, and [tex]\( T \)[/tex] is the time period in years.
3. Set up the equation using the given conditions:
Since the interest is equal to the principal, we have:
[tex]\[
I = P
\][/tex]
Substituting the values, we get:
[tex]\[
6300 = \frac{6300 \times R \times 10}{100}
\][/tex]
4. Rearrange the equation to solve for [tex]\( R \)[/tex]:
First, eliminate the principal from both sides by dividing by 6300:
[tex]\[
1 = \frac{R \times 10}{100}
\][/tex]
5. Simplify the equation:
[tex]\[
1 = \frac{10R}{100}
\][/tex]
Multiply both sides by 100 to clear the fraction:
[tex]\[
100 = 10R
\][/tex]
6. Solve for [tex]\( R \)[/tex]:
Divide both sides by 10:
[tex]\[
R = \frac{100}{10} = 10
\][/tex]
Therefore, the rate percent at which the interest on Rs. 6300 in 10 years is equal to the principal is [tex]\( 10\% \)[/tex].
