Ram invested P in scheme A and 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. Respective ratio between the interest earned from scheme A and that earned from scheme B was 8 : 21.
Quantity :
I. Rate of interest offered by scheme A.
II. Rate of interest offered by scheme C (simple interest p.a.), when 1,600/- is invested for 3 years earns an interest of 384/-.

$$S.I. = \frac{P \times R \times T}{100}$$

$$C.I. = P [(1 + \frac{R}{100})^T - 1]$$

Rate of interest for scheme B = 10 %

Time period in each scheme = 2 years

Acc to ques,

=> $$\frac{\frac{P \times R \times 2}{100}}{2P [(1 + \frac{10}{100})^2 - 1]} = \frac{8}{21}$$

=> $$\frac{\frac{R}{50}}{\frac{21}{50}} = \frac{8}{21}$$

=> $$\frac{R}{21} = \frac{8}{21}$$

=> $$R = 8 \%$$

Quantity I = 8 %

Quantity II : $$384 = \frac{1600 \times R \times 3}{100}$$

=> $$R = \frac{384}{48} = 8 \%$$

$$\therefore$$ Quantity I = Quantity II