Let rate = R% per annum and Time = T years, T. D. = True Discount, P. W. = Present Worth Then,
1. P.W. = 100 x Amount/100 + (R x T) = 1100 x T.D./(R x T)
2. T.D. = (P.W.) x R x T./100 = Amount x R x T/100 + (R x T)
3. Sum = (S.I.) x (T.D.)/(S.I.)  (T.D.)
4. (S.I.)  (T.D.) = S.I. on T.D.
5. When the sum is put at compound interest, then P.W. = Amount/(1 + R/100)^{T}
1. 

C.P. = Rs. 3000
S.P. = Rs.[(3600 x 100)/(100) + (10 x 2)] = Rs. 3000.
Gain = 0%.
2. 

P.W. = Rs. (2562  122) = Rs. 2440.
S.I. on Rs. 2440 for 4 months is Rs. 122.
Rate = [(100 x 122)/(2440 x 1/3)]% = 15%
3. 

Required money= P.W. of Rs. 10028 due 9 months hence =
Rs.[(10028 x 100)/(100 + 12 x (9/12)] = Rs. 9200.
4. 

P.W. of Rs. 12,880 due 8 months hence= Rs.[(12880 x 100)/(100 + 18 x (8/12)]
P.W. of Rs. 12,880 due 8 months hence = Rs. (12880 x 100)/112
P.W. of Rs. 12,880 due 8 months hence = Rs. 11500
5. 

S.I. on Rs. (110  10) for a certain time = Rs. 10.
S.I. on Rs. 100 for double the time = Rs. 20.
T.D. on Rs. 120 = Rs. (120  100) = Rs. 20.
T.D. on Rs. 110 = Rs.(20/120) x 110 = Rs. 18.33
6. 

S.P. = 102% of Rs. 600 = [(102/100) x 600] = Rs. 612.
Now, P.W. = Rs. 612 and sum = Rs. 688.50.
T.D. = Rs. (688.50  612) = Rs. 76.50.
Thus, S.I. on Rs. 612 for 9 months is Rs. 76.50.
Rate = [(100 x 76.50)/(612 x 3/4)]% = 16(2/3)%
7. 

Let P.W. be Rs. X
Then, S.I. on Rs. x at 16% for 9 months = Rs. 189.
X x 16 x (9/12) x (1/100) = 189 or X = 1575.
P.W. = Rs. 1575.
Sum due = P.W. + T.D. = Rs. (1575 + 189) = Rs. 1764.
8. 

S.P.= P.W. of Rs. 2200 due 1 year hence = Rs. [(2200 x 100)/(100 + (10 x 1))]
S.P.= P.W. of Rs. 2200 due 1 year hence = Rs. 2000.
Gain = Rs. (2000  1950) = Rs. 50.
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