S.I. for `1 1/2` years =  Rs. (1067.20 - 1012) = Rs. 55.20

S.I. for `2 1/2` years  = Rs. `(55.20 xx 2/3 xx 5/2)` = Rs. 92

`:.`      principal  = Rs.  (1012 - 92)  = Rs. 920

Hence , rate =  `((100 xx 92 xx 2)/(920 xx 5))` = 4%

Let sum  = `x` , Then , S.I.  = `x`

`:.`    Time  = `((100 xx S.I.)/(P xx R))`

=`((100 xx x)/(x xx 12))` years =  `8 1/3` years =  8 years 4 months.

S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205

S.I. for  5 years = Rs. `(2205/3 xx 5)` = Rs. 3675.

`:.`    principal  = Rs. (9800 - 3675) = Rs. 6125.

Hence ,rate  = `((100 xx 3675)/(6125 xx 5))`% =   12%

S.I. for 5 years = Rs. (1020 - 720) = Rs. 300.

S.I. for 2 years = Rs. `(300/5 xx 2)` = Rs. 120

`:.`       principal  = Rs. (720 - 120) = Rs. 600.

S.I. for 1 year = Rs.  ( 854 - 815) = Rs. 39

S.I. for 3 years = Rs. (39 x 3) = Rs. 117

`:.`      principal  = Rs. (815 - 117) = 698.

Let the sum be Rs. 100 , Then

S.I.  for first 6 months = Rs.`((100 xx 10 xx 1)/(100 xx 2))`  = Rs . 5.

S.I. for last 6 months = Rs.  `((105 xx 10 xx 1)/(100 xx 2))` = Rs. 5.25

So, amount at the end of 1 year =  Rs. (100 + 5 + 5.25) = Rs. 110.25

`:.`      Effective  rate  = (110.25 - 100) = 10.25%

S.I. = Rs. `(10 xx 3/100 xx 4)` = Rs. 1.20.

Let the sum be Rs. `x` Now , S.I. = Rs. 600,  T = 10 years.

Rate = `((100 xx 600)/(x xx 10))% =  (6000/x)`%

S.I. for first 5 years = Rs  `((x xx 5 xx 6000)/(x xx 100))`  = Rs. 300

S.I. for last 5 years = Rs. `(3x xx 5 xx (6000)/(x xx 100))` = Rs. 900

`:.`      Total interest = Rs.  (900 + 300) = Rs. 1200

Let the sum be Rs. `x` , Then ,

`((x xx 6 xx 3)/(100)) + ((x xx 9 xx 5)/(100)) + ((x xx 13 xx 3)/(100))`  = 8160

`hArr       18x + 45x + 39x = (8160  xx 100)`

`hArr        102x =  816000`

`hArr        x =  8000`

Let the  principal  be  P and rate of interest be R%

`:.`         Required ratio =` [((P xx R xx 6)/(100))/((P xx R xx 9)/(100))]`

     = `(6PR)/(9PR) =  6/9` = 2 : 3