Peter invested an amount of ₹ 12,000 at the rate of 10 p.c.p.a. simple interest and another amount at the rate of 20 p.c.p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14 p.c.p.a. Find the total amount invested.
(a)₹ 20,000
(b)₹ 22,000
(c)₹ 24,000
(d)₹ 25,000
(e)None of these
Answer
Answer (as printed): A
Explanation
Let the second amount be ₹ $x$. Then, $$\begin{aligned} & \left(\frac{12000 \times 10 \times 1}{100}\right)+\left(\frac{x \times 20 \times 1}{100}\right)=\left[\frac{(12000+x) \times 14 \times 1}{100}\right] \\ & \Leftrightarrow 12000+20 x=168000+14 x \\ & \Leftrightarrow \quad 6 x=48000 \Leftrightarrow x=8000 . \\ & \therefore \quad \text { Total investment }=₹(12000+8000)=₹ 20000 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.