Let the sum be Rs, P, Then
`P[(1 + 5/100)^4 - 1] - (P xx 10 xx 2)/(100)` = 124.05
`rArr P[(21/20)^4 - 1 - 1/5] = 124.05`
`rArr P[194481/160000 - 6/5] = 12405/100`
`rArr P[(194481 - 192000)/(160000)] = 12405/100`
`rArr P = (12405/100 xx 160000/2481)` = 8000.
Difference in C.I. and S.I. for 2 years = Rs. 32
S.I. for one years = Rs. 400
`:.` S.I. on Rs. 400 for one year = Rs. 32
So, Rate = ` ((100 xx 32)/(400 xx 1))`% = 8%
Hence , difference in C.I. and S.I. for 3rd year
= S.I. on Rs. 832 = Rs. `((832 xx 8 xx 1)/(100))` = Rs. 66.56.
Total difference = Rs. (32 + 66.56) = Rs. 98.56
Let the sum be Rs. `x `, Then ,
C.I. = `[x (1 + 4/100)^2 - x]`
=`(676/625 x - x)` = ` 51/625 x`
S.I. = `((x xx 4 xx 2)/(100)) = (2x)/(25)`
`:.` ` (51x)/(625) - (2x)/(25)` = 1.
or `x` = 625.
`[15000 xx (1 + R/100)^2 - 15000] - ((15000 xx R xx 2)/(1000))` = 96
`hArr 15000[(1 + R/100)^2 -1 - (2R)/(100)]`= 96
`hArr 15000[((100 + R)^2 - 10000 - 200R)/(10000)]` = 96
`hArr R^2 = (96 xx 2)/(3)`
`hArr R^2 = 64`
`hArr R = 8`
`:.` Rate = 8%.
Let P = Rs. 100, Then S.I. Rs. 60 and T = 6 years
`:.` R =` (100 xx 60)/(100 xx 6) = 10%p.a.`
Now, P = Rs. 12000, T = 3 years and R = 10% p.a.
`:.` C.I. = Rs. `[12000 xx {(1 + 10/100)^3 - 1}]`
=Rs. `(12000 xx 331/1000)` = Rs. 3972.
C.I. = Rs `[4000 xx (1 + 10/100)^2 - 4000]`
=Rs.`(4000xx 11/10 xx 11/10 - 4000)`
=Rs. 840.
`:.` Sum = Rs.`((420 xx100)/(- 3 xx 8))`
Rs. 1750.
Let the sum be Rs. P , Then
`[P(1 + 10/100)^2 - P] = 525`
`hArr P[(11/10)^2 - 1] = 525`
`hArr P = ((525 xx 100)/(21))` = 2500
`:.` Sum = Rs. 2500
So , S.I. = Rs. `((2500 xx 5 xx 4)/(100)) ` = Rs. 500
Let the sum be Rs. P , Then
`[P(1 + (25)/(2 xx 100))^2 - P]` = 510
or `P[(9/8)^2 - 1] = 510`
or `p = ((510 xx 64)/(17)) = 1920.`
`:.` Sum = Rs. 1920.
So S.I. = Rs.`((1920 xx 25 xx 2)/(2 xx 100))` = Rs. 480.
Let the time be n years, Then ,
800 x `(1 + 5/100)^2n = 926.10`
or `(1 + 5/100)^2n = 9261/8000`
or `(21/20)^2n = (21/20)^3`
or 2n = 3
or `n = 3/2`
or n = `1 1/2`
`:.` n = `1 1/2`years
Present worth = Rs. `[(169)/((1 + 4/100))^2]`
= Rs. `(169 xx 25/26 xx 25/26)`
= Rs. 156.25
