On what sum of money will the difference between simple interest and compound interest for 2 years at 5\% per annum be equal to ₹ 63? [SSC-CHSL (10 + 2) Exam, 2015]
(a)₹ 24600
(b)₹ 24800
(c)₹ 25200
(d)₹ 25500
Answer
Answer (as printed): C
Explanation
Time $=2$ years Rate of interest = 5\% per annum According to question, $$\begin{aligned} & P\left[\left(1+\frac{r}{100}\right)^{n}-1\right]-\frac{P \times r \times t}{100}=63 \\ & P\left[\left(1+\frac{5}{100}\right)^{2}-1\right]-\frac{P \times 5 \times 2}{100}=63 \\ & \Rightarrow P\left[\left(1+\frac{5}{100}\right)^{2}-1\right]-\frac{10 P}{100}=63 \\ & \Rightarrow P\left[\left(\frac{105}{100}\right)^{2}-1\right]-\frac{10 P}{100}=63 \\ & \Rightarrow P\left(\frac{11025-10000}{10000}\right)-\frac{10 P}{100}=63 \\ & \Rightarrow \frac{1025 P}{10000}-\frac{10 P}{100}=63 \\ & \Rightarrow \frac{1025 P-1000 P}{10000}=63 \\ & \Rightarrow 25 \mathrm{P}=₹ 630000 \\ & \Rightarrow P=\frac{630000}{25}=₹ 25200 \end{aligned}$$ Hence, sum = ₹ 25200
Explanation as extracted from the printed page; notation may be imperfect.