Let each instalmnt be Rs. `x` , then , `( x + (x xx 12 xx 1)/(100)) + (x + (x xx 12 xx 2)/(100)) + x ` = 1092
`hArr (28x)/(25) + (31x)/(25) + x` = 1092
`hArr (28x + 31x + 25x)` = (1092 x 25)
`hArr 84 x` = 1092 x 25
`hArr x = ((1092 xx 25)/(84)) ` = 325
`:.` Each instalment = Rs. 325
Let sum = P and original rate = R. Then ,` [{P xx (R + 2) xx 3)/(100)] - [(P xx R xx 3)/(100)]` = 360
`hArr` 3PR + 6P - 3PR = 3600
`hArr` 6P = 36000
`hArr` P = 6000.
Hence , sum = Rs. 6000
Let he sum be Rs. `x`, Then , `((x xx 10 xx 7)/(100 xx 2)) - ((x xx 12 xx 5)/(100 xx 2))` = 40.
`hArr (7x)/(20) - (3x)/(10) = 40 hArr x` = (40 x 20) = 800
Hence ,the sum is Rs. 800
Let sum = Rs. `x` , Then , S.I. = Rs. `(4x)/(9)`
Let rate = R% and time = R years.
Then , `((x xx R xx R)/(100)) = (4x)/(9)`
or `R^2 = 400/9 or R = 20/3 = 6 2/3`
`:.` Rate =` 6 2/3`% and Time = `6 2/3` years = 6 years 8 months.
Let principal = P, Then , S.I. = P and T = 16 yers.
`:.` Rate = `((100 xx P)/(P xx 16))`% = `6 1/4`% p.a.
S.I. for `1 1/2` years = Rs. (1164 - 1008) = Rs. 156
S.I. for 2 years = Rs. `(156 xx 2/3 xx 2)` = Rs. 208
`:.` principal = Rs. (1008 - 208) = Rs. 800
Now , p. = 800, T = 2 and S.I. = 208
`:.` Rate = `((100 xx 208)/(800 xx 2))`% = 13%
Let the sum borrowed be `x` .then,
`((x xx 6 xx 2)/(100)) + ((x xx 9 xx 3)/(100)) + ((x xx 14 xx 4)/(100))` = 11400
`hArr ((3x)/(25) + (27x)/(100) + (14x)/(25)) ` = 11400
`hArr (95x)/(100) = 11400`
`hArr` x = `((11400 xx 100)/(95))` = 12000
Hence , sum borrowed = Rs. 12,000
S.I. = Rs. (920 - 800) = Rs. 120 ,P. = Rs. 800, T = 3 years
`:.` R = `((100 xx 120)/(800 xx 3))`% = 5%
New rate = (5 + 3)% = 8%
New S.I. = Rs.` ((800 xx 8 xx 3)/(100))` = Rs. 192
`:.` New amount = Rs. (800 + 192) = Rs. 992.
Let sum be Rs. `x` then ,S.I. = Rs. `(x 27/2 xx 4 xx 1/100)` = Rs. `(27x)/(50) `
`:.` Amount = Rs. `(x + (27x)/(50)) = Rs. (77x)/(50)`
`:.` `(77x)/(50)` = 2502.50 `hArr x = (2502.50 xx 50)/(77) ` = 1625
Hence , sum = Rs. 1625.
Time = (24 + 31 + 18) days = 73 days = `73/365` year = `1/5` year.
P = Rs. 3000 and R = `6 1/4`% p.a. = `25/4` % p.a.
`:.` S.I. = Rs. `(3000 xx 25/4 xx 1/5 xx 1/100)` = Rs. 37.50.
