Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is

Answer: Option B

Explanation:

Let the Sum be P
$$\begin{aligned} S.I. = \frac{P*4*2}{100} = \frac{2P}{25}\\ C.I. = P(1+\frac{4}{100})^2 - P \\ = \frac{676P}{625} - P \\ = \frac{51P}{625} \\ \text{As, C.I. - S.I = 1}\\ => \frac{51P}{625} - \frac{2P}{25} = 1 \\ => \frac{51P - 50P}{625} = 1 \\ P = 625 \end{aligned}$$

Answer: Option C

Explanation:

$$\begin{aligned} S.I. = \frac{1000*10*4}{100} = 400 \\ C.I. = [1000(1+\frac{10}{100})^4 - 1000] \\ = 464.10 \end{aligned}$$

So difference between simple interest and compound interest will be 464.10 - 400 = 64.10

Answer: Option D

Explanation:

Let Rate will be R%

$$\begin{aligned} 1200(1+\frac{R}{100})^2 = \frac{134832}{100} \\ (1+\frac{R}{100})^2 = \frac{134832}{120000} \\ (1+\frac{R}{100})^2 = \frac{11236}{10000} \\ (1+\frac{R}{100}) = \frac{106}{100} \\ => R = 6\% \end{aligned}$$

Answer: Option C

Explanation:

$$\begin{aligned} S.I. = \frac{P*R*T}{100} \\ P = \frac{50*100}{5*2} = 500\\ Amount = 500(1+\frac{5}{100})^2 \\ 500(\frac{21}{20} * \frac{21}{20}) \\ = 551.25 \\ C.I. = 551.25 - 500 = 51.25 \end{aligned}$$

Answer: Option B

Explanation:

$$\begin{aligned} C.I. = (4000 \times(1+\frac{10}{100})^2 - 4000) \\ = 4000 * \frac{11}{10} * \frac{11}{10} - 4000 \\ = 840 \\ \text{So S.I. = } \frac{840}{2} = 420\\ \text{So Sum = } \frac{S.I. * 100}{R*T} \\ = \frac{420 * 100}{3*8} \\ = Rs 1750 \end{aligned}$$