Sapna invested Rs. 20,700 on simple interest, partly at 9% per annum and partly at 14% per annum. If she earns equal interests from the two investments after 3 years, then find the sum invested at 9% per annum (in Rs.).

Correct option is A

Given:

Total investment = ₹20,700.
Part at 9% p.a. = x, part at 14% p.a. = 20700 - x.
Simple interest from both parts is equal after 3 years.

Formula Used:
Simple Interest SI = $$P \times R \times T$$ 

Solution:​
Equality condition: $$x \times 9 \times 3 = (20700 - x) \times 14 \times$$​3​

0.09x = 0.14(20700 - x)
0.09x = 2898 - 0.14x

0.23x = 2898

x =$$\frac{2898}{0.23} =$$12600 

Alternate Solution: ​

For equal SI and for equal time 

​$$\frac{P_1}{P_2} = \frac{R_2}{R_1}$$ 

where P = principle, R = rate of interest 

​$$\frac{P_1}{P_2} = \frac{14}{9}$$ 

Now, 

​$$P_1 + P_2 = 20700 \\ \ \\ (14 + 9)unit = 20700 \\ \ \\ 23 unit = 20700 \\ \ \\ 1 unit = \frac{20700}{23} = 900$$ 

So, P₁ = 900 × 14 = Rs. 12600