A certain sum of money is invested at an interest rate of 5\% per annum and a second sum, twice as large as the first, is invested at 5.5\% p.a. The total amount of interest earned from the two investments together is ₹ 1000 per year and the interest is withdrawn every year. The second sum invested is
(a)₹ 6250
(b)₹ 10500
(c)₹ 12500
(d)₹ 15000
Answer
Answer (as printed): C
Explanation
Let the two sums be ₹ $x$ and ₹ $2 x$. Then, $\frac{x \times 5}{100}+\frac{2 x \times 5.5}{100}=1000$ $$\begin{aligned} & \Rightarrow \quad 5 x+11 x=100000 \\ & \Rightarrow \quad 16 x=100000 \Rightarrow x=6250 . \end{aligned}$$ Hence, second sum ₹ $(6250 \times 2)=₹ 12500$.
Explanation as extracted from the printed page; notation may be imperfect.