Answer : Option A

Explanation :

Let the investment in scheme A be Rs.x
and the investment in scheme B be Rs.(13900 - x)
$MF#%\begin{align}&\text{We know that }\text{SI = }\dfrac{\text{PRT}}{100}\\\\ &\text{Simple Interest for Rs.x in 2 years at 14% p.a. = }\dfrac{x \times 14 \times 2}{100} = \dfrac{28x}{100}\\\\ &\text{Simple Interest for Rs.(13900 - x) in 2 years at 11% p.a. = }\dfrac{(13900 - x) \times 11 \times 2}{100} = \dfrac{22(13900 - x)}{100}\\\\ &\text{Total interest = Rs.3508}\\\\ &\dfrac{28x}{100} + \dfrac{22(13900 - x)}{100} = 3508\\\\ &28x + 305800 -22x = 350800\\\\ &6x = 45000\\\\ &x = \dfrac{45000}{6} = 7500\end{align}$MF#%
Investment in scheme B = 13900 - 7500 = Rs.6400

Answer : Option D

Explanation :

$MF#%\text{Time,T = 2 year 5 months = 29 months = }\dfrac{29}{12}\text{ year}\\\\ \text{SI} = \dfrac{\text{PRT}}{100} = \dfrac{7500 \times 11 \times \dfrac{29}{12}}{100} = 75 \times 11 \times \dfrac{29}{12} = 1993.75$MF#%

Let rate = R% and time = R years.

Then, 1200 x R x R = 432 100

12R² = 432

R² = 36

R = 6.

Answer : Option C

Explanation :

P = ?
R = x%
Simple Interest,SI = x
T = x years
$MF#%\text{P}=\dfrac{100 \times \text{SI}}{\text{RT}} = \dfrac{100 \times x}{x \times x} = \dfrac{100}{x} $MF#%

Answer : Option B

Explanation :

Let the automobile financier lends Rs.100
$MF#%\text{Simple Interest for first 6 months = }\dfrac{\text{PRT}}{100}= \dfrac{100 \times 10 \times \dfrac{1}{2}}{100}=\text{Rs. }5$MF#%
After 6 months, he adds the simple interest to principal
i.e., after 6 months, principal becomes Rs.100 + Rs.5 = Rs.105
$MF#%\text{Simple Interest for next 6 months = }\dfrac{\text{PRT}}{100}= \dfrac{105 \times 10 \times \dfrac{1}{2}}{100}=\text{Rs. }5.25$MF#%
Amount at the end of 1 year = Rs.105 + Rs. 5.25 = Rs.110.25
i.e., Effective Simple Interest he gets for Rs.100 for 1 year = 110.25 - 100 = 10.25
i.e, the Effective Rate of Interest = 10.25%
$MF#%\color{#F00}{(∵ \text{R = }\dfrac{100 \times \text{SI}}{\text{PT}} = \dfrac{100 \times 10.25}{100 \times 1} = 10.25\%)}$MF#%

Answer : Option A

Explanation :

$MF#%\text{Simple Interest, SI = }\dfrac{\text{PRT}}{100} = \dfrac{3200 \times 10 \times \dfrac{40}{365} }{100} = 35.07$MF#%

Time = (24+31+18)days = 73 days = 73/365 years = 1/5 years.
P = Rs.3000 and R = 6 1/4%p.a = 25/4%p.a
S.I. = Rs.(3,000*(25/4)*(1/5)*(1/100))= Rs.37.50.

S.I. for 1½years = Rs.(1164-1008) = Rs.156
S.l. for 2 years = Rs.(156*(2/3)*2)=Rs.208
Principal = Rs. (1008 - 208) = Rs. 800
Now, P = 800, T = 2 and S.l. = 208
Rate =(100* 208)/(800*2)% = 13%

S.l. = Rs. (920 - 800) = Rs. 120; p = Rs. 800, T = 3 yrs.
R = ((100 x 120)/(800*3) ) % = 5%.
New rate = (5 + 3)% = 8%.
New S.l. = Rs. (800*8*3)/100 = Rs. 192
New amount = Rs.(800+192) = Rs. 992

Let sum = P and original rate = R.
[ (P*(R+2)*3)/100]-[ (P*R*3)/100] = 360
3PR + 6P - 3PR = 36000
6P=36000
P=6000