Investment Breakdown

Let the total investment be $P = ₹21,700$.

Let the sum invested at 3% per annum be $P_1$.

Let the sum invested at 12% per annum be $P_2$.

We know that $P_1 + P_2 = P$, so $P_1 + P_2 = 21700$.

Interest Calculation

The time period for both investments is $T = 7$ years.

The interest rates are $R_1 = 3\% = 0.03$ and $R_2 = 12\% = 0.12$.

The formula for Simple Interest (SI) is $SI = \frac{P \times R \times T}{100}$.

Interest from the first investment ($SI_1$) is $\frac{P_1 \times 3 \times 7}{100}$.

Interest from the second investment ($SI_2$) is $\frac{P_2 \times 12 \times 7}{100}$.

Finding the Sum at 3%

The problem states that the interests earned are equal: $SI_1 = SI_2$.

Therefore, $\frac{P_1 \times 3 \times 7}{100} = \frac{P_2 \times 12 \times 7}{100}$.

Simplifying the equation:

• $21 P_1 = 84 P_2$
• $P_1 = \frac{84}{21} P_2$
• $P_1 = 4 P_2$

Now we have a system of two equations:

1. $P_1 + P_2 = 21700$
2. $P_1 = 4 P_2$

Substitute the second equation into the first:

$4 P_2 + P_2 = 21700$

$5 P_2 = 21700$

$P_2 = \frac{21700}{5} = 4340$

Now, calculate $P_1$ using $P_1 = 4 P_2$:

$P_1 = 4 \times 4340 = 17360$

The sum invested at 3% per annum is ₹17,360.