A part of ₹ 9600 is invested at a 5\% annual return, while the remainder is invested at a 3\% annual return. If the annual income from both portions is the same, what is the total income from the two investments?
(a)₹ 320
(b)₹ 380
(c)₹ 410
(d)₹ 440
(e)None of these
Answer
Answer (as printed): E
Explanation
Let the sum invested at 5\% be ₹ $x$ and that invested at $3 \%$ be ₹ $(9600-x)$. Then, 5\% of $x=3 \%$ of ( $9600-x$ ) $$\begin{aligned} & \Rightarrow \quad 5 x=3(9600-x) \\ & \Rightarrow \quad 8 x=28800 \Rightarrow x=3600 . \end{aligned}$$ Hence, total income $=5 \%$ of $x+3 \%$ of $(9600-x)$ $$\begin{aligned} & =₹(5 \% \text { of } 3600+3 \% \text { of } 6000) \\ & =₹(180+180)=₹ 360 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.