1. **Problem Statement:** Two capitals of 300000 and 700000 are invested for the same duration at an interest rate of 7% per annum. The total interest earned is 105000. We need to find the common duration in months. 2. **Formula Used:** Simple interest formula: $$I = P \times r \times t$$ where $I$ is interest, $P$ is principal, $r$ is rate per year (in decimal), and $t$ is time in years. 3. **Step-by-step Solution:** - Let the common duration be $t$ months. - Convert $t$ months to years: $$t_{years} = \frac{t}{12}$$ - Calculate interest from first capital: $$I_1 = 300000 \times 0.07 \times \frac{t}{12}$$ - Calculate interest from second capital: $$I_2 = 700000 \times 0.07 \times \frac{t}{12}$$ - Total interest is given as 105000, so: $$I_1 + I_2 = 105000$$ $$300000 \times 0.07 \times \frac{t}{12} + 700000 \times 0.07 \times \frac{t}{12} = 105000$$ 4. **Simplify the equation:** $$0.07 \times \frac{t}{12} \times (300000 + 700000) = 105000$$ $$0.07 \times \frac{t}{12} \times 1000000 = 105000$$ 5. **Solve for $t$:** $$\frac{0.07 \times 1000000 \times t}{12} = 105000$$ $$\frac{70000 \times t}{12} = 105000$$ $$70000 \times t = 105000 \times 12$$ $$70000 \times t = 1260000$$ $$t = \frac{1260000}{70000}$$ $$t = 18$$ 6. **Answer:** The common duration of investment is **18 months**.