A certain sum is invested for 5 years at 6% Simple interest per annum in Scheme A. When half of that sum is invested for 5 years at 8% Simple interest per annum in Scheme B, it yie... A certain sum is invested for 5 years at 6% Simple interest per annum in Scheme A. When half of that sum is invested for 5 years at 8% Simple interest per annum in Scheme B, it yields an interest which is Rs 724 less than the interest received from Scheme A. What is the sum invested in Scheme A? Read more

Steps to Solve

1. Identify the variables Let the total sum invested in Scheme A be $P$. Thus, when half of that sum is invested in Scheme B, it becomes $\frac{P}{2}$.

2. Calculate the interest from Scheme A The interest from Scheme A, which is invested at 6% for 5 years, can be calculated using the formula for simple interest: $$ I_A = P \times \frac{6}{100} \times 5 $$ Simplifying this gives: $$ I_A = \frac{30P}{100} = 0.3P $$

3. Calculate the interest from Scheme B The interest from Scheme B is calculated with the same formula, where the principal is $\frac{P}{2}$, the rate is 8%, and the time is 5 years: $$ I_B = \left(\frac{P}{2}\right) \times \frac{8}{100} \times 5 $$ Simplifying this gives: $$ I_B = \frac{40P}{200} = 0.2P $$

4. Set up the equation based on the given condition According to the problem, the interest from Scheme B is Rs 724 less than the interest from Scheme A: $$ I_B = I_A - 724 $$ Substituting the interests: $$ 0.2P = 0.3P - 724 $$

5. Solve for P Rearranging the equation: $$ 0.3P - 0.2P = 724 $$ This simplifies to: $$ 0.1P = 724 $$ Dividing both sides by 0.1 yields: $$ P = 7240 $$