1.A certain sum amounts to Rs.7350 in 2 yrs and to Rs.8575 in 3 yrs.Find the sum and rate%?
sol:
S.I. on Rs.7350 for 1yr =Rs.(8575-7350)
=Rs.1225
S.I. on Rs.7350 for 2yrs=Rs.2*1225
=Rs.2450
PTR/100=2450
=>P*2*R/100=2450
Since S.I. on Rs.7350 for 1yr =Rs.(8575-7350)
=Rs.1225
Rate R=100*1225/(7350*10
=16 2/3%
Since it is C.I ,Let sum be Rs.X
Then X[1+(R/100)]2=7350
=>X[1+(50/100)]2=7350
=>X=7350*(36/49)
Sum=Rs.5400
2.If the difference between C.I compounded halfyearly and S.I on a sum at 10% per annum for one yr is Rs.25 the sum is
sol:p[1+((R/2)/100)]2n-PTR/100=25
P[1+((10/2)/100)]2n-P*1*10/100=25
=>P=Rs.400
3.A man borrowed Rs.800 at 10 % per annum S.I and immediately lent the whole sum at 10% per annum C.I What does he gain at the end of 2yrs?
sol:
C.I.=Rs.[800[1+(10/100)2]-800]=Rs.168
S.I=Rs.[800*10*2/100]=Rs.160
Gain=C.I-S.I=Rs(168-160)
=Rs.8
4.On what sum of money will be S.I for 3 yrs at 8% per annum be half of C.I on Rs.400 for 2 yrs at 10% per annum?
sol:
C.I on Rs.400 for 2yrs at 10%=Rs.[400*[1+(10/100)]2-400]
=Rs.84
Required S.I =1/2*84=42/-
New S.I=Rs.42,Time=3yrs Rate=8%
Sum=Rs.[100*42/(3*8)]
=Rs.175
5.A sum of money placed at C.I doubles itself in 5yrs .It will amount to 8 times itself in-------------
sol:
p[1+(R/100)]5=2P
=>[1+(R/100)]5=2
To become 8 times =>8P
p[1+(R/100)]5=2^3P
=[1+(R/100)]^(5*3)
=[1+(R/100)]^15
n=15years.
sol:
S.I. on Rs.7350 for 1yr =Rs.(8575-7350)
=Rs.1225
S.I. on Rs.7350 for 2yrs=Rs.2*1225
=Rs.2450
PTR/100=2450
=>P*2*R/100=2450
Since S.I. on Rs.7350 for 1yr =Rs.(8575-7350)
=Rs.1225
Rate R=100*1225/(7350*10
=16 2/3%
Since it is C.I ,Let sum be Rs.X
Then X[1+(R/100)]2=7350
=>X[1+(50/100)]2=7350
=>X=7350*(36/49)
Sum=Rs.5400
2.If the difference between C.I compounded halfyearly and S.I on a sum at 10% per annum for one yr is Rs.25 the sum is
sol:p[1+((R/2)/100)]2n-PTR/100=25
P[1+((10/2)/100)]2n-P*1*10/100=25
=>P=Rs.400
3.A man borrowed Rs.800 at 10 % per annum S.I and immediately lent the whole sum at 10% per annum C.I What does he gain at the end of 2yrs?
sol:
C.I.=Rs.[800[1+(10/100)2]-800]=Rs.168
S.I=Rs.[800*10*2/100]=Rs.160
Gain=C.I-S.I=Rs(168-160)
=Rs.8
4.On what sum of money will be S.I for 3 yrs at 8% per annum be half of C.I on Rs.400 for 2 yrs at 10% per annum?
sol:
C.I on Rs.400 for 2yrs at 10%=Rs.[400*[1+(10/100)]2-400]
=Rs.84
Required S.I =1/2*84=42/-
New S.I=Rs.42,Time=3yrs Rate=8%
Sum=Rs.[100*42/(3*8)]
=Rs.175
5.A sum of money placed at C.I doubles itself in 5yrs .It will amount to 8 times itself in-------------
sol:
p[1+(R/100)]5=2P
=>[1+(R/100)]5=2
To become 8 times =>8P
p[1+(R/100)]5=2^3P
=[1+(R/100)]^(5*3)
=[1+(R/100)]^15
n=15years.
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