Sujata invested ₹ 7500 at simple interest @ 11 p.c.p.a. She further invested some amount at simple interest @ 15 p.c.p.a. Total interest earned at the end of the year became 12 p.c.p.a. Find the amount invested at the rate of 15 p.c.p.a.
(a)₹ 2000
(b)₹ 2500
(c)₹ 3000
(d)₹ 3500
Answer
Answer (as printed): B
Explanation
Let the required sum be ₹ $x$. Then, $11 \%$ of $7500+15 \%$ of $x=12 \%$ of $(7500+x)$$$\begin{aligned} & \Rightarrow \quad\left(\frac{11}{100} \times 7500\right)+\left(\frac{15}{100} x\right)=\frac{12}{100}(7500+x) \\ & \Rightarrow \quad 82500+15 x=90000+12 x \Rightarrow 3 x=7500 \\ & \Rightarrow \quad x=2500 \end{aligned}$$ Hence, required sum $=₹ 2500$.
Explanation as extracted from the printed page; notation may be imperfect.