Amount to be paid  = Rs. `(100 + (200 xx 5 xx 1)/(100) + (100 xx 5 xx 1)/(100))` =  Rs. 115.

Rs. 10 + S.I.  on Rs. 10 for 11 monhs

= Rs. 11 + S.I. on Re. 1 for (1 + 2 + 3 + 4 + ................+ 10) months

`rArr  `     Rs.  10 + S.I.  of Re. 1 for 110 months =  Rs. 11 + S.I.   on  Re. 1 for  55 months

`rArr` S.I. on Re.  1 for 55 months = Re. 1

`:.`Rate = `((100 xx 12)/(1 xx 55))`% = `21 9/11`%

Let the annual instalment be Rs. `x`  Then ,

`[ x + ((x xx 3 xx 5)/(100))] + [x + ((x xx 2 xx 5)/(100))] + [x + ((x xx 1 xx 5)/(100))] + x = 6450`

`hArr     (23x)/(20) + (22x)/(20) + (21x)/(20) + x =  6450`

`hArr      86x = 6450 xx 20`

`hArr      x =  1500`

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

`((x xx 8 xx 1)/(100) - (x xx 31/4 xx 1/100)` =  6150

`hArr    32x - 31x = 6150 xx 4`

`hArr      x = 24600`

Let the sum be Rs.  `x` , Then ,

`(x xx 25/2 xx 1/100) - ((x xx 10 xx 1)/(100))` = 1250

`hArr       25x - 20x =  250000`

`hArr        5x = 250000`

`hArr        x = 50000`

Let the sum be Rs. `x` and original rate be  R% . Then ,

`(x xx (R + 3) xx 2)/(100) - (x xx R xx 2)/(100) ` = 72

`hArr     2Rx + 6x - 2Rx = 7200`

`hArr      6x = 7200`

`hArr       x =  1200`

Let the savings be  X and Y and the rates of simple interest be `5x` and `4x`  respectively .

Then , `X xx 5x xx 1/2 xx 1/100 =  Y xx 4x xx 1/2 xx 1/100`

or `X/Y = 4/5` , i.e.,

X : Y =  4 : 5

S.I.  = Rs. `(2600 xx 20/3 xx 1/100 xx T) `

=Rs. `(520/3 xx T)`

which is an exact number of rupees when  T = 3

Let the second amount be Rs. `x`, Then ,

`((12000 xx 10 xx 1)/(100)) + ((x xx 20 xx 1)/(100))` = `((( 12000 + x) xx 14 xx 1)/(100))`

`hArr      12000 + 20x = 168000 + 14x`

`hArr       6x =  48000`

`hArr        x = 8000`

`:.`          Total investment = Rs. (12000 + 8000) = Rs. 20000

`((1500 xx R_1 xx 3)/(100)) - ((1500 xx R_2 xx 3)/(100))` = 13.50

`hArr        4500(R_1 - R_2) =  1350`

`hArr    R_1 - R_2 =  1350/4500`

`hArr      R_1 - R_2 `= 0.3%.