The compound interest on a certain sum of money for 2 years at 10\% per annum is ₹ 525. The simple interest on the same sum of money for double the time at half the rate percent per annum is? [RBI Gr. 'B' (Phase I) Exam, 2015]
(a)₹ 1000
(b)₹ 500
(c)₹ 200
(d)₹ 800
Answer
Answer (as printed): B
Explanation
Let the sum of money be ₹ P $$\begin{aligned} & \text { Then }\left[\mathrm{P}\left(1+\frac{\mathrm{R}}{100}\right)^{\mathrm{t}}-\mathrm{P}\right]=\mathrm{CI} \\ & \quad\left[\mathrm{P}\left(1+\frac{10}{100}\right)^{2}-\mathrm{P}\right]=525 \\ & \Rightarrow\left(\frac{11}{10}\right)^{2}-1=525 \\ & \Rightarrow \mathrm{P}\left(\frac{121}{100}-1\right)=525 \\ & \Rightarrow \mathrm{P}\left(\frac{21}{100}=525\right) \\ & \Rightarrow \mathrm{P}=\left(\frac{525 \times 100}{21}\right)=₹ 2500 \\ & \therefore \text { Sum of money }=₹ 2500 . \end{aligned}$$ Simple interest on the same sum ₹ 2500 for 4 (double the time) years at 5\% (half the rate of percent per annum) is $$\text { So, S.I. }=₹\left(\frac{2500 \times 5 \times 4}{100}\right)=₹ 500$$
Explanation as extracted from the printed page; notation may be imperfect.