Explanation:

Let rate = R% and time = R years.

Then,  1200 * R * R 100 = 432

12 R 2 = 432

=> R 2 = 36 ? R = 6

Let each installment be Rs.x. Then, 

(P.W. of Rs.x due 1 year hence) + (P.W of Rs.x due 2 years hence) + (P.W of Rs. X due 3 years hence) = 7620.

x 1 + 50 3 x 100 + x 1 + 50 3 x 100 2 + x 1 + 50 3 x 100 3 = 7620

  6 x 7 + 36 x 49 + 216 x 343 = 7620

  294 x + 252 x + 216 x = 7620 x 343

 => x = 3430

 Amount of each installment = Rs.3430

I . P * R * 5 100 = P ? R = 20

  I I . P 1 + R 100 2 - P - P * R * 2 100 = 400 = > p R 2 = 4000000

  I I I . P * R * 1 100 = 2000 = > P R = 200000

  P R 2 P R = 4000000 200000 ? R = 20

Thus I only or (II and III) give answer.

 Correct answer is (D)

Compound Interest on P at 10% for 2 years when interest is compounded half-yearly

= P 1 + R 2 100 2 T - P = P 1 + 1 20 4 - P = P 21 20 4 - P

Simple Interest on P at 10% for 2 years =  P R T 100 = P × 10 × 2 100 = P 5

Given that difference between compound interest and simple interest = 124.05

  P * 21 20 4 - P - P 5 = 124 . 05

=> P 21 20 4 - 1 - 1 5 = 124 . 05

 P=8000

Clearly, Rate = 5% p.a., Time = 3 years, S.I.= Rs. 1200. . .
So principal=RS [100*1200]/3*5=RS 8000
Amount = Rs. 8000 x [1 +5/100]^3 - = Rs. 9261.
.. C.I. = Rs. (9261 - 8000) = Rs. 1261.

Interest for 1 year is the same whether it's simple interest or the compound interest.

Now interest of third year = 8575 - 7350 = 1225; means principal for this interest is 7350 if comound interest is takenIf 7350 is the principal interest = 1225

if 100 is the principal interest =(1225/7350) * 100 = 50/3 %

When a thing increases for two successive times the overall increase on initial amount = a + b + (a * b)/100

Therefore overall interest for two years = 50/3 + 50/3 + [(50/3)*(50/3)]/100 = 325/9 %

Therefore amount after 2 years = 100 + 325/9 = 1225/9

If 1225/9 is the amount principal =100

if 7350 is the amount principal =(900/1225)*7350 =5400

So sum = 5400; Rate = 50/3 %

Principal = Rs. 16000; Time = 9 months =3 quarters;
Rate = 20% per annum = 5% per quarter.
Amount = Rs. [16000 x (1+(5/100))3] = Rs. 18522.

CJ. = Rs. (18522 - 16000) = Rs. 2522

P 1 + r 100 4 P 1 + r 100 5 = 1 1 + r 100 = 100 100 + r = 100 120 = 5 6 

difference in C.I and S.I in 2years =Rs.32

S.I for 1year =Rs.400

S.I for Rs.400 for one year =Rs.32

rate=[100*32)/(400*1)%=8%

difference between in C.I and S.I for 3rd year

=S.I on Rs.832= Rs.(832*8*1)/100=Rs.66.56

Principal = Rs. 1000; Amount = Rs. 1331; Rate = 10% p.a. Let the time be n years. Then,
[ 1000 (1+ (10/100))^n ] = 1331 or (11/10)^n = (1331/1000) = (11/10)^3
n = 3 years