Question : Sudeep invested $\frac{1}{8}$th of a certain sum at 5% p.a. for two years and $\frac{3}{5}$th of the sum at 6% p.a. for two years and the remaining at 10% p.a. for two years. If the total interest received is INR 1,674, then the total sum invested is:
Option 1: INR 13,000
Option 2: INR 12,000
Option 3: INR 10,500
Option 4: INR 12,500
Correct Answer: INR 12,000
Solution : Let total sum be INR $x$. Remaining part $=x - \frac{x}{8} - \frac{3x}{5}=\frac{40x - 5x - 24x}{40}=\frac{11x}{40}$ According to the question ⇒ $\frac{(x × \frac{1}{8} × 5 × 2)}{100} + \frac{(x × \frac{3}{5} × 6 × 2)}{100} + \frac{(x × \frac{11}{40} × 10 × 2)}{100} = 1674$ ⇒ $\frac{5x}{400} + \frac{36x}{500} + \frac{11x}{200} = 1674$ ⇒ $\frac{25x + 144x + 110x}{2000} = 1674$ ⇒ $\frac{279x}{2000} = 1674$ $\therefore x = 12000$ Hence, the correct answer is INR 12000.
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