Ram invested Rs. P in scheme A and Rs. 2P in scheme B, for two years each. Scheme A offers simple interest p.a. Scheme B offers compound interest (compounded annually) at the rate of 10% p.a. The ratio between the interest earned from scheme A and that earned from scheme B was 8 : 21. I. Rate of interest offered by scheme A. II. Rate of interest offered by scheme C (simple interest p.a.), when Rs. 1,600 is invested for 3 years earns an interest of Rs.384.

Question

Accepted Answer

Step-by-step explanation:

1. Interest from scheme A (simple interest): For principal $P$, rate $r\%$ p.a., time 2 years,

$I_A = P\cdot \frac{r}{100}\cdot 2 = \frac{2Pr}{100}.$

2. Interest from scheme B (compound interest 10% p.a., annually): Principal $2P$, 2 years,

Amount $=2P(1.1)^2=2P\cdot1.21=2.42P$, so

$I_B=2.42P-2P=0.42P=\frac{42P}{100}.$

3. Given $I_A:I_B=8:21$, so

$\dfrac{I_A}{I_B}=\dfrac{8}{21}$. Substitute the expressions:

$\dfrac{\frac{2Pr}{100}}{\frac{42P}{100}}=\dfrac{8}{21} \Rightarrow \dfrac{2r}{42}=\dfrac{8}{21} \Rightarrow \dfrac{r}{21}=\dfrac{8}{21} \Rightarrow r=8.$

Thus Quantity I = $8\%$.

4. Quantity II: Simple interest where $P=1600$, $t=3$ years and interest $=384$:

$384=1600\cdot \dfrac{r}{100}\cdot 3 = 4800\cdot \dfrac{r}{100} = 48r \Rightarrow r=\dfrac{384}{48}=8.$

Thus Quantity II = $8\%$.

Therefore Quantity I = Quantity II.

FINAL_ANSWER: d

Answer

Answer

Answer

Answer