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Solutions :-
1)
Given that
Principal = Rs. 8000
Rate of interest = 10%
Time = 5 years
We know that
Simple Interest = PTR/100
=> S.I. = (8000×10×5)/100
=> S.I. = 80×10×5
=> Simple Interest = Rs. 4000
We know that
Amount = Principal + Interest
=> Amount = 8000+4000
Therefore, Amount = Rs. 12000
2)
Let the Principal be Rs. X
Given that
Rate of interest = 6%
Time = 5 years
Simple Interest = Rs. 60
We know that
Simple Interest = PTR/100
=> 60 = (X×6×5)/100
=> 60 = 30X/100
=> 60 = 3X/10
=> 3X = 60×10
=> 3X = 600
=> X = 600/3
=> X = 200
Therefore, Principal = Rs. 200
3)
Given that
Principal = Rs. 2600
Simple Interest = Rs. 288
Rate of interest = 8%
Let the time be T years
We know that
T = (100×I)/PR
=> T = (100×288)/(2600×8)
=> T = 28800/20800
=> T = 288/208
=> T = 18/13 years
Required Time = 18/13 years
4)
Given that
Principal = Rs. 50
Amount = Rs. 55
Rate of interest = 4%
Simple Interest = Amount - Principal
=> S.I = 55-50 = Rs. 5
Let the time be T years
T = (100×I)/PR
=> T = (100×5)/(50×4)
=> T = 500/200
=> T = 5/2 years
Required time is 5/2 years
5)
Given that
Amount = Rs. 1080
Principal = Rs. 900
Simple Interest = 1080-900 = Rs. 180
Time = 3 years
We know that
Rate of interest = (100×I)/PT
=> R = (100×180)/(3×900)
=> R = 18000/2700
=> R = 180/27
=> R = 20/3
=> R = 6 2/3 %
Required rate of interest = 6 2/3%
6)
Given that
Principal = Rs. 500
Rate of interest = 14%
Time = 18 months = 18/12 years
= 3/2 years
We know that
Simple Interest = PTR/100
=> S.I = (500×3×14)/(100×2)
=> S.I. = 5×3×7
=> S.I. = Rs. 105
The simple Interest = Rs. 105
7)
Given that
Time = 16 years
Let the Principal be Rs.X
Amount = Rs. 2X
Simple Interest = 2X-X = Rs.X
We know that
S.I. = PTR/100
=> X = (X×16×R)/100
=> 100X = 16XR
=> R = 100X/16X
=> R = 100/16
=> R = 25/4%
Rate of interest = 25/4%
8)
Given that
Principal = Rs. 650
Amount = Rs. 812.50
Simple Interest = 812.50-650
= Rs. 162.50
Rate of interest = 6 1/4% = 25/4 %
We know that
T = (100×I)/PR
=> T = (100×162.50)/(650×25/4)
=> T = (16250×4)/(650×25)
=> T = 65000/(650×25)
=> T = 100/25
=> T = 4 years
Required time = 4 years
9)
Given that
Principal = Rs.300
Rate of interest = 6%
Time = 6 years
We know that
S.I. = PTR/100
=> S.I. = (300×6×6)/100
=> S.I. = 3×6×6
=> S.I. = 108
Simple Interest = Rs. 108
Amount = 300+108 = Rs. 408
Amount = Rs. 408
10)
Given that
Principal = Rs. 200
Rate of Interest = 5 1/2 % = 11/2%
Time = 2 years
We know that
Simple Interest = PTR/100
=> S.I. = (200×11×2)/(2×100)
=> S.I. = 22
Simple Interest = Rs. 22
Amount = 200+22 = Rs. 222
Required amount = Rs. 222