If the compound interest on a sum for 2 years at $12 \frac{1}{2} \%$ per annum is ₹ 510, the simple interest on the same sum at the same rate for the same period of time is :
(a)₹ 400
(b)₹ 450
(c)₹ 460
(d)₹ 480
Answer
Answer (as printed): D
Explanation
Let the sum be ₹ $P$. Then, $\left[P\left(1+\frac{25}{2 \times 100}\right)^{2}-P\right]=510$ $$\Rightarrow P\left[\left(\frac{9}{8}\right)^{2}-1\right]=510 \Rightarrow P=\left(\frac{510 \times 64}{17}\right)=1920 .$$ $\therefore$ Sum $=₹ 1920$. So, $\mathrm{S} . \mathrm{I} .=₹\left(\frac{1920 \times 25 \times 2}{2 \times 100}\right)=₹ 480$.
Explanation as extracted from the printed page; notation may be imperfect.