Page 1
Q u e s t i o n : 1
Find the simple interest and the amount when:
Principal = Rs 6400, rate = 6% p.a. and time = 2 years
S o l u t i o n :
P = Rs. 6400, R = 6%, T = 2 years
S. I. =
P×R×T
100
=
6400×6×2
100
= Rs. 768
Amount=P+S.I.
=6400+768 = Rs. 7168
Q u e s t i o n : 2
Find the simple interest and the amount when:
Principal = Rs 2650, rate = 8% p.a. and time = 2
1
2
years
S o l u t i o n :
P = Rs. 2650, R = 8%, T=2
1
2
years =
5
2
years
S.I. =
P×R×T
100
=
2650×8×5
100×2
= Rs. 530
Amount = P +S. I.
=2650+530 = Rs. 3180
Q u e s t i o n : 3
Find the simple interest and the amount when:
Principal = Rs 1500, rate = 12% p.a. and time = 3 years 3 months.
S o l u t i o n :
P = Rs. 1500, R = 12%, T = 3 +
3
12
=
13
4
years
S.I. =
P×R×T
100
=
1500×12×13
100×4
= Rs. 585
Amount=P+S.I.
=1500+585 =Rs . 2085
Q u e s t i o n : 4
Find the simple interest and the amount when:
Principal = Rs 9600, rate = 7
1
2
%
p.a. and time = 5 months.
S o l u t i o n :
P = Rs. 9600R = 7
1
2
% T = 5 months =
5
12
yearsS. I. =
P×R×T
100
=
9600×15×5
100×2×12
= Rs. 300Amount = P + S. I. = 9600 +300 = Rs. 9900
Q u e s t i o n : 5
Find the simple interest and the amount when:
Principal = Rs 5000, rate = 9% p.a. and time = 146 days.
S o l u t i o n :
P = Rs. 5000 , R = 9% , T = 146 days =
146
365
years
S .I . =
P×R×T
100
=
5000×9×146
100×365
=Rs. 180
Amount=P+S .I .
=5000+180 =Rs . 5180
Q u e s t i o n : 6
Find the time when:
Principal = Rs 6400, SI = Rs 1152 and rate = 6% p.a.
S o l u t i o n :
P = Rs. 6400, S. I. = Rs. 1152, R = 6%
T =
S.I.×100
P×R
=
1152×100
6400×6
=
1152
384
= 3 years
Q u e s t i o n : 7
Find the time when:
Principal = Rs 9540, SI = Rs 1908 and rate = 8% p.a.
S o l u t i o n :
P = Rs. 9540 , S. I. = Rs. 1908, R = 8%
T =
S.I.×100
P×R
=
1908×100
9540×8
=
10
4
=2
1
2
years
Page 2
Q u e s t i o n : 1
Find the simple interest and the amount when:
Principal = Rs 6400, rate = 6% p.a. and time = 2 years
S o l u t i o n :
P = Rs. 6400, R = 6%, T = 2 years
S. I. =
P×R×T
100
=
6400×6×2
100
= Rs. 768
Amount=P+S.I.
=6400+768 = Rs. 7168
Q u e s t i o n : 2
Find the simple interest and the amount when:
Principal = Rs 2650, rate = 8% p.a. and time = 2
1
2
years
S o l u t i o n :
P = Rs. 2650, R = 8%, T=2
1
2
years =
5
2
years
S.I. =
P×R×T
100
=
2650×8×5
100×2
= Rs. 530
Amount = P +S. I.
=2650+530 = Rs. 3180
Q u e s t i o n : 3
Find the simple interest and the amount when:
Principal = Rs 1500, rate = 12% p.a. and time = 3 years 3 months.
S o l u t i o n :
P = Rs. 1500, R = 12%, T = 3 +
3
12
=
13
4
years
S.I. =
P×R×T
100
=
1500×12×13
100×4
= Rs. 585
Amount=P+S.I.
=1500+585 =Rs . 2085
Q u e s t i o n : 4
Find the simple interest and the amount when:
Principal = Rs 9600, rate = 7
1
2
%
p.a. and time = 5 months.
S o l u t i o n :
P = Rs. 9600R = 7
1
2
% T = 5 months =
5
12
yearsS. I. =
P×R×T
100
=
9600×15×5
100×2×12
= Rs. 300Amount = P + S. I. = 9600 +300 = Rs. 9900
Q u e s t i o n : 5
Find the simple interest and the amount when:
Principal = Rs 5000, rate = 9% p.a. and time = 146 days.
S o l u t i o n :
P = Rs. 5000 , R = 9% , T = 146 days =
146
365
years
S .I . =
P×R×T
100
=
5000×9×146
100×365
=Rs. 180
Amount=P+S .I .
=5000+180 =Rs . 5180
Q u e s t i o n : 6
Find the time when:
Principal = Rs 6400, SI = Rs 1152 and rate = 6% p.a.
S o l u t i o n :
P = Rs. 6400, S. I. = Rs. 1152, R = 6%
T =
S.I.×100
P×R
=
1152×100
6400×6
=
1152
384
= 3 years
Q u e s t i o n : 7
Find the time when:
Principal = Rs 9540, SI = Rs 1908 and rate = 8% p.a.
S o l u t i o n :
P = Rs. 9540 , S. I. = Rs. 1908, R = 8%
T =
S.I.×100
P×R
=
1908×100
9540×8
=
10
4
=2
1
2
years
Q u e s t i o n : 8
Find the time when:
Principal = Rs 5000, amount = Rs 6450 and rate = 12% p.a.
S o l u t i o n :
P = Rs. 5000, A=Rs. 6450, R = 12%
S. I. = A -P
= 6450 -5000
= Rs. 1450
T =
S.I×100
P×R
=
1450×100
5000×12
=
29
12
= 2
5
12
=2 years 5 months
Q u e s t i o n : 9
Find the rate when:
Principal = Rs 8250, SI = Rs 1100 and time = 2 years.
S o l u t i o n :
P = Rs. 8250, S. I. = Rs. 1100, T = 2 years
R=
S.I.×100
P×T
=
1100×100
8250×2
=
1100
165
=6.67%
Q u e s t i o n : 1 0
Find the rate when:
Principal = Rs 5200, SI = Rs 975 and time = 2
1
2
years.
S o l u t i o n :
P= Rs. 5200 , S.I.=Rs. 975 [ T=2
1
2
years=
5
2
years]
R=
S.I.×100
P×T
=
975×100×2
5200×5
=
195
26
=7.5%
Q u e s t i o n : 1 1
Find the rate when:
Principal = Rs 3560, amount = Rs 4521.20 and time = 3 years.
S o l u t i o n :
P = Rs. 3560 , A = Rs. 4521. 20 , T = 3 years
S. I. = A -P = 4521. 20 -3560
= Rs. 961. 20
R =
S.I.×100
P×T
=
961.20×100
3560×3
=
96120×100
100×3560×3
=9%
Q u e s t i o n : 1 2
Shanta borrowed Rs 6000 from the State Bank of India for 3 years 8 months at 12% per annum. What amount will clear off her debt?
S o l u t i o n :
P = Rs 6000, R = 12%, T=3 years 8 months = 3
8
12
=
44
12
years
S.I. =
P×R×T
100
=
6000×12×44
100×12
= Rs 2640
A = P +S. I.
= 6000 +2640
= Rs 8640
Q u e s t i o n : 1 3
Hari borrowed Rs 12600 from a moneylender at 15% per annum simple interest. After 3 years, he paid Rs 7070 and gave a goat to clear off the debt. What is the cost of the goat?
S o l u t i o n :
P = Rs. 12600 R = 15% T = 3 years
S.I.=
P×R×T
100
=
12600×15×3
100
=Rs. 5670
A = Rs. 12600 +Rs. 5670 = Rs. 18270
Hari had to pay Rs. 18270 to the money lender, but he paid Rs. 7070 and a goat.
? Cost of the goat = Rs. 18270 -Rs. 7070
= Rs. 11200
Q u e s t i o n : 1 4
The simple interest on a certain sum for 3 years at 10% per annum is Rs 829.50. Find the sum.
S o l u t i o n :
Page 3
Q u e s t i o n : 1
Find the simple interest and the amount when:
Principal = Rs 6400, rate = 6% p.a. and time = 2 years
S o l u t i o n :
P = Rs. 6400, R = 6%, T = 2 years
S. I. =
P×R×T
100
=
6400×6×2
100
= Rs. 768
Amount=P+S.I.
=6400+768 = Rs. 7168
Q u e s t i o n : 2
Find the simple interest and the amount when:
Principal = Rs 2650, rate = 8% p.a. and time = 2
1
2
years
S o l u t i o n :
P = Rs. 2650, R = 8%, T=2
1
2
years =
5
2
years
S.I. =
P×R×T
100
=
2650×8×5
100×2
= Rs. 530
Amount = P +S. I.
=2650+530 = Rs. 3180
Q u e s t i o n : 3
Find the simple interest and the amount when:
Principal = Rs 1500, rate = 12% p.a. and time = 3 years 3 months.
S o l u t i o n :
P = Rs. 1500, R = 12%, T = 3 +
3
12
=
13
4
years
S.I. =
P×R×T
100
=
1500×12×13
100×4
= Rs. 585
Amount=P+S.I.
=1500+585 =Rs . 2085
Q u e s t i o n : 4
Find the simple interest and the amount when:
Principal = Rs 9600, rate = 7
1
2
%
p.a. and time = 5 months.
S o l u t i o n :
P = Rs. 9600R = 7
1
2
% T = 5 months =
5
12
yearsS. I. =
P×R×T
100
=
9600×15×5
100×2×12
= Rs. 300Amount = P + S. I. = 9600 +300 = Rs. 9900
Q u e s t i o n : 5
Find the simple interest and the amount when:
Principal = Rs 5000, rate = 9% p.a. and time = 146 days.
S o l u t i o n :
P = Rs. 5000 , R = 9% , T = 146 days =
146
365
years
S .I . =
P×R×T
100
=
5000×9×146
100×365
=Rs. 180
Amount=P+S .I .
=5000+180 =Rs . 5180
Q u e s t i o n : 6
Find the time when:
Principal = Rs 6400, SI = Rs 1152 and rate = 6% p.a.
S o l u t i o n :
P = Rs. 6400, S. I. = Rs. 1152, R = 6%
T =
S.I.×100
P×R
=
1152×100
6400×6
=
1152
384
= 3 years
Q u e s t i o n : 7
Find the time when:
Principal = Rs 9540, SI = Rs 1908 and rate = 8% p.a.
S o l u t i o n :
P = Rs. 9540 , S. I. = Rs. 1908, R = 8%
T =
S.I.×100
P×R
=
1908×100
9540×8
=
10
4
=2
1
2
years
Q u e s t i o n : 8
Find the time when:
Principal = Rs 5000, amount = Rs 6450 and rate = 12% p.a.
S o l u t i o n :
P = Rs. 5000, A=Rs. 6450, R = 12%
S. I. = A -P
= 6450 -5000
= Rs. 1450
T =
S.I×100
P×R
=
1450×100
5000×12
=
29
12
= 2
5
12
=2 years 5 months
Q u e s t i o n : 9
Find the rate when:
Principal = Rs 8250, SI = Rs 1100 and time = 2 years.
S o l u t i o n :
P = Rs. 8250, S. I. = Rs. 1100, T = 2 years
R=
S.I.×100
P×T
=
1100×100
8250×2
=
1100
165
=6.67%
Q u e s t i o n : 1 0
Find the rate when:
Principal = Rs 5200, SI = Rs 975 and time = 2
1
2
years.
S o l u t i o n :
P= Rs. 5200 , S.I.=Rs. 975 [ T=2
1
2
years=
5
2
years]
R=
S.I.×100
P×T
=
975×100×2
5200×5
=
195
26
=7.5%
Q u e s t i o n : 1 1
Find the rate when:
Principal = Rs 3560, amount = Rs 4521.20 and time = 3 years.
S o l u t i o n :
P = Rs. 3560 , A = Rs. 4521. 20 , T = 3 years
S. I. = A -P = 4521. 20 -3560
= Rs. 961. 20
R =
S.I.×100
P×T
=
961.20×100
3560×3
=
96120×100
100×3560×3
=9%
Q u e s t i o n : 1 2
Shanta borrowed Rs 6000 from the State Bank of India for 3 years 8 months at 12% per annum. What amount will clear off her debt?
S o l u t i o n :
P = Rs 6000, R = 12%, T=3 years 8 months = 3
8
12
=
44
12
years
S.I. =
P×R×T
100
=
6000×12×44
100×12
= Rs 2640
A = P +S. I.
= 6000 +2640
= Rs 8640
Q u e s t i o n : 1 3
Hari borrowed Rs 12600 from a moneylender at 15% per annum simple interest. After 3 years, he paid Rs 7070 and gave a goat to clear off the debt. What is the cost of the goat?
S o l u t i o n :
P = Rs. 12600 R = 15% T = 3 years
S.I.=
P×R×T
100
=
12600×15×3
100
=Rs. 5670
A = Rs. 12600 +Rs. 5670 = Rs. 18270
Hari had to pay Rs. 18270 to the money lender, but he paid Rs. 7070 and a goat.
? Cost of the goat = Rs. 18270 -Rs. 7070
= Rs. 11200
Q u e s t i o n : 1 4
The simple interest on a certain sum for 3 years at 10% per annum is Rs 829.50. Find the sum.
S o l u t i o n :
Let the sum be Rs. P.
S.I. = Rs. 829. 50, T = 3 years, R = 10%
Now, P=
S.I×100
R×T
=
829.50×100
10×3
=
8295
3
= 2765Hence, the sum is Rs. 2765.
Q u e s t i o n : 1 5
A sum when reckoned at 7
1
2
%
per annum amounts to Rs 3920 in 3 years. Find the sum
S o l u t i o n :
Let the required sum be Rs. x.
A = Rs. 3920, R = 7
1
2
%, T = 3 years
Now,
Now, S.I.=
P×R×T
100
=
x×15×3
2×100
=
9x
40
A = P +S. I.
= x +
9x
40
=
40x+9x
40
=
49x
40
But the amount is Rs. 3920.
= >
49x
40
= 3920
= > x =
3920×40
49
=
156800
49
= 3200
Hence, the required sum is Rs. 3200.
Q u e s t i o n : 1 6
A sum of money put at 11% per annum amounts to Rs 4491 in 2 years 3 months. What will it amount to in 3 years at the same rate?
S o l u t i o n :
Given: R=11%, T=2 years 3 months = 2+
3
12
=
27
12
years
Let the required sum be Rs. x.
S.I.=
P×R×T
100
=
x×11×27
9
100×12 4
=
99x
400
A = P +S. I.
= x +
99x
400
=
400x+99x
400
=
499x
400
But the amount is Rs. 4491.
= >
499x
400
= 4491
= > x =
4491×400
499
=
1796400
499
= 3600
Hence, the required sum is Rs. 3600.
? S.I.=
P×R×T
100
=
3600×11×3
100
= Rs. 1188
? Amount=P+S.I.=3600+1188
=Rs. 4788
Q u e s t i o n : 1 7
A sum of money invested at 8% per annum amounts to Rs 12122 in 2 years. What will it amount to in 2 years 8 months at 9% per annum?
S o l u t i o n :
Let the required sum be Rs. x.
S.I.=
P×R×T
100
=
x×8×2
100
=
16x
100
A = P +S. I.
= x +
16x
100
=
100x+16x
100
=
116x
100
But the amount is Rs. 12122.
= >
116x
100
= 12122
= > x =
12122×100
116
= 10450
Now, S.I.=
P×R×T
100
=
10450×9
3
×32
8
100×12 4 1 = Rs. 2508
? A=P+S.I.
= Rs. 10450 + Rs. 2508
= Rs. 12958
Q u e s t i o n : 1 8
At what rate per cent per annum will Rs 3600 amount to Rs 4734 in 3
1
2
years?
S o l u t i o n :
P = Rs. 3600 A = Rs. 4734 T= 3
1
2
=
7
2
years
S. I. = A -P
= 4734 -3600
= Rs. 1134
R=
S.I.×100
P×T
=
1134×100×2
3600×7
=9%
Q u e s t i o n : 1 9
If Rs 640 amounts to Rs 768 in 2 years 6 months, what will Rs 850 amount to in 3 years at the same rate per cent per annum?
S o l u t i o n :
Page 4
Q u e s t i o n : 1
Find the simple interest and the amount when:
Principal = Rs 6400, rate = 6% p.a. and time = 2 years
S o l u t i o n :
P = Rs. 6400, R = 6%, T = 2 years
S. I. =
P×R×T
100
=
6400×6×2
100
= Rs. 768
Amount=P+S.I.
=6400+768 = Rs. 7168
Q u e s t i o n : 2
Find the simple interest and the amount when:
Principal = Rs 2650, rate = 8% p.a. and time = 2
1
2
years
S o l u t i o n :
P = Rs. 2650, R = 8%, T=2
1
2
years =
5
2
years
S.I. =
P×R×T
100
=
2650×8×5
100×2
= Rs. 530
Amount = P +S. I.
=2650+530 = Rs. 3180
Q u e s t i o n : 3
Find the simple interest and the amount when:
Principal = Rs 1500, rate = 12% p.a. and time = 3 years 3 months.
S o l u t i o n :
P = Rs. 1500, R = 12%, T = 3 +
3
12
=
13
4
years
S.I. =
P×R×T
100
=
1500×12×13
100×4
= Rs. 585
Amount=P+S.I.
=1500+585 =Rs . 2085
Q u e s t i o n : 4
Find the simple interest and the amount when:
Principal = Rs 9600, rate = 7
1
2
%
p.a. and time = 5 months.
S o l u t i o n :
P = Rs. 9600R = 7
1
2
% T = 5 months =
5
12
yearsS. I. =
P×R×T
100
=
9600×15×5
100×2×12
= Rs. 300Amount = P + S. I. = 9600 +300 = Rs. 9900
Q u e s t i o n : 5
Find the simple interest and the amount when:
Principal = Rs 5000, rate = 9% p.a. and time = 146 days.
S o l u t i o n :
P = Rs. 5000 , R = 9% , T = 146 days =
146
365
years
S .I . =
P×R×T
100
=
5000×9×146
100×365
=Rs. 180
Amount=P+S .I .
=5000+180 =Rs . 5180
Q u e s t i o n : 6
Find the time when:
Principal = Rs 6400, SI = Rs 1152 and rate = 6% p.a.
S o l u t i o n :
P = Rs. 6400, S. I. = Rs. 1152, R = 6%
T =
S.I.×100
P×R
=
1152×100
6400×6
=
1152
384
= 3 years
Q u e s t i o n : 7
Find the time when:
Principal = Rs 9540, SI = Rs 1908 and rate = 8% p.a.
S o l u t i o n :
P = Rs. 9540 , S. I. = Rs. 1908, R = 8%
T =
S.I.×100
P×R
=
1908×100
9540×8
=
10
4
=2
1
2
years
Q u e s t i o n : 8
Find the time when:
Principal = Rs 5000, amount = Rs 6450 and rate = 12% p.a.
S o l u t i o n :
P = Rs. 5000, A=Rs. 6450, R = 12%
S. I. = A -P
= 6450 -5000
= Rs. 1450
T =
S.I×100
P×R
=
1450×100
5000×12
=
29
12
= 2
5
12
=2 years 5 months
Q u e s t i o n : 9
Find the rate when:
Principal = Rs 8250, SI = Rs 1100 and time = 2 years.
S o l u t i o n :
P = Rs. 8250, S. I. = Rs. 1100, T = 2 years
R=
S.I.×100
P×T
=
1100×100
8250×2
=
1100
165
=6.67%
Q u e s t i o n : 1 0
Find the rate when:
Principal = Rs 5200, SI = Rs 975 and time = 2
1
2
years.
S o l u t i o n :
P= Rs. 5200 , S.I.=Rs. 975 [ T=2
1
2
years=
5
2
years]
R=
S.I.×100
P×T
=
975×100×2
5200×5
=
195
26
=7.5%
Q u e s t i o n : 1 1
Find the rate when:
Principal = Rs 3560, amount = Rs 4521.20 and time = 3 years.
S o l u t i o n :
P = Rs. 3560 , A = Rs. 4521. 20 , T = 3 years
S. I. = A -P = 4521. 20 -3560
= Rs. 961. 20
R =
S.I.×100
P×T
=
961.20×100
3560×3
=
96120×100
100×3560×3
=9%
Q u e s t i o n : 1 2
Shanta borrowed Rs 6000 from the State Bank of India for 3 years 8 months at 12% per annum. What amount will clear off her debt?
S o l u t i o n :
P = Rs 6000, R = 12%, T=3 years 8 months = 3
8
12
=
44
12
years
S.I. =
P×R×T
100
=
6000×12×44
100×12
= Rs 2640
A = P +S. I.
= 6000 +2640
= Rs 8640
Q u e s t i o n : 1 3
Hari borrowed Rs 12600 from a moneylender at 15% per annum simple interest. After 3 years, he paid Rs 7070 and gave a goat to clear off the debt. What is the cost of the goat?
S o l u t i o n :
P = Rs. 12600 R = 15% T = 3 years
S.I.=
P×R×T
100
=
12600×15×3
100
=Rs. 5670
A = Rs. 12600 +Rs. 5670 = Rs. 18270
Hari had to pay Rs. 18270 to the money lender, but he paid Rs. 7070 and a goat.
? Cost of the goat = Rs. 18270 -Rs. 7070
= Rs. 11200
Q u e s t i o n : 1 4
The simple interest on a certain sum for 3 years at 10% per annum is Rs 829.50. Find the sum.
S o l u t i o n :
Let the sum be Rs. P.
S.I. = Rs. 829. 50, T = 3 years, R = 10%
Now, P=
S.I×100
R×T
=
829.50×100
10×3
=
8295
3
= 2765Hence, the sum is Rs. 2765.
Q u e s t i o n : 1 5
A sum when reckoned at 7
1
2
%
per annum amounts to Rs 3920 in 3 years. Find the sum
S o l u t i o n :
Let the required sum be Rs. x.
A = Rs. 3920, R = 7
1
2
%, T = 3 years
Now,
Now, S.I.=
P×R×T
100
=
x×15×3
2×100
=
9x
40
A = P +S. I.
= x +
9x
40
=
40x+9x
40
=
49x
40
But the amount is Rs. 3920.
= >
49x
40
= 3920
= > x =
3920×40
49
=
156800
49
= 3200
Hence, the required sum is Rs. 3200.
Q u e s t i o n : 1 6
A sum of money put at 11% per annum amounts to Rs 4491 in 2 years 3 months. What will it amount to in 3 years at the same rate?
S o l u t i o n :
Given: R=11%, T=2 years 3 months = 2+
3
12
=
27
12
years
Let the required sum be Rs. x.
S.I.=
P×R×T
100
=
x×11×27
9
100×12 4
=
99x
400
A = P +S. I.
= x +
99x
400
=
400x+99x
400
=
499x
400
But the amount is Rs. 4491.
= >
499x
400
= 4491
= > x =
4491×400
499
=
1796400
499
= 3600
Hence, the required sum is Rs. 3600.
? S.I.=
P×R×T
100
=
3600×11×3
100
= Rs. 1188
? Amount=P+S.I.=3600+1188
=Rs. 4788
Q u e s t i o n : 1 7
A sum of money invested at 8% per annum amounts to Rs 12122 in 2 years. What will it amount to in 2 years 8 months at 9% per annum?
S o l u t i o n :
Let the required sum be Rs. x.
S.I.=
P×R×T
100
=
x×8×2
100
=
16x
100
A = P +S. I.
= x +
16x
100
=
100x+16x
100
=
116x
100
But the amount is Rs. 12122.
= >
116x
100
= 12122
= > x =
12122×100
116
= 10450
Now, S.I.=
P×R×T
100
=
10450×9
3
×32
8
100×12 4 1 = Rs. 2508
? A=P+S.I.
= Rs. 10450 + Rs. 2508
= Rs. 12958
Q u e s t i o n : 1 8
At what rate per cent per annum will Rs 3600 amount to Rs 4734 in 3
1
2
years?
S o l u t i o n :
P = Rs. 3600 A = Rs. 4734 T= 3
1
2
=
7
2
years
S. I. = A -P
= 4734 -3600
= Rs. 1134
R=
S.I.×100
P×T
=
1134×100×2
3600×7
=9%
Q u e s t i o n : 1 9
If Rs 640 amounts to Rs 768 in 2 years 6 months, what will Rs 850 amount to in 3 years at the same rate per cent per annum?
S o l u t i o n :
P = Rs. 640, A = Rs. 768, T=2 years 6 months =
5
2
years
S. I. = A -P
= 768 -640
= Rs. 128
R=
S.I.×100
P×T
=
128×100×2
640×5
=8%
P = Rs. 850, R = 8%, T = 3 years
? S.I. =
P×R×T
100
=
850×8×3
100
=
2040
10
=Rs. 204
? A = P +S. I.
= 850 +204
= Rs. 1054
Q u e s t i o n : 2 0
In what time will Rs 5600 amount to Rs 6720 at 8% per annum?
S o l u t i o n :
P = Rs. 5600, A = Rs. 6720, R = 8%
S. I. = A -P
= 6720 -5600
= Rs. 1120
T=
S.I.×100
P×R
=
1120×100
5600×8
=
1120
448
=2
1
2
years
Q u e s t i o n : 2 1
A sum of money becomes
8
5
of itself in 5 years at a certain rate of simple interest. Find the rate of interest.
S o l u t i o n :
Let the sum be Rs. x .
Amount=
8x
5
? S.I.=A -P=
8x
5
-x
=
3x
5
Let the rate be R%.
S.I.=
P×R×T
100
= >
3x
5
=
x×R×5
1
100 20
= > 3x ×20 = R ×x ×5
= > R =
3×x×20
4
x×5
= 12
Hence, the rate of interest is 12 %.
Q u e s t i o n : 2 2
A sum of money lent at simple interest amounts to Rs 783 in 2 years and to Rs 837 in 3 years. Find the sum and the rate per cent per annum.
S o l u t i o n :
Amount in 3 years = (Principal + S. I. for 3 years) = Rs. 837
Amount in 2 years = (Principal + S. I. for 2 years) = Rs. 783
On subtracting:
S. I. for 1 year = (837 -783) = Rs. 54
S. I. for 2 years=
54
1
×2 = Rs. 108
? Sum = Amount for 2 years -S. I. for 2 years
= 783 -108
= Rs. 675
P = Rs. 675, S. I. = Rs. 108 and T = 2 years
R =
S.I.×100
P×T
=
108×100
50 2
675 27 ×2 1
= 8%
Q u e s t i o n : 2 3
A sum of money lent at simple interest amount to Rs 4745 in 3 years and to Rs 5475 in 5 years. Find the sum and the rate per cent per annum.
S o l u t i o n :
Amount in 5 years = (Principal + S. I. for 5 years) = Rs. 5475
Amount in 3 years = (Principal + S. I. for 3 years) = Rs. 4745
On subtracting:
S. I. for 2 years = (5475 -4745) = Rs. 730
S. I. for 3 years=
730
2
×3 = Rs. 1095
? Sum = Amount for 3 years -S. I. for 3 years
= 4745 -1095
= Rs. 3650
P=Rs. 3650, S.I.=Rs. 1095, T=3 years
R=
S.I.×100
P×T
=
1095×100
3650×3
= 10%
Q u e s t i o n : 2 4
Divide Rs 3000 into two parts such that the simple interest on the first part for 4 years at 8% per annum is equal to the simple interest on the second part for 2 years at 9% per annum.
S o l u t i o n :
( )
( )
Page 5
Q u e s t i o n : 1
Find the simple interest and the amount when:
Principal = Rs 6400, rate = 6% p.a. and time = 2 years
S o l u t i o n :
P = Rs. 6400, R = 6%, T = 2 years
S. I. =
P×R×T
100
=
6400×6×2
100
= Rs. 768
Amount=P+S.I.
=6400+768 = Rs. 7168
Q u e s t i o n : 2
Find the simple interest and the amount when:
Principal = Rs 2650, rate = 8% p.a. and time = 2
1
2
years
S o l u t i o n :
P = Rs. 2650, R = 8%, T=2
1
2
years =
5
2
years
S.I. =
P×R×T
100
=
2650×8×5
100×2
= Rs. 530
Amount = P +S. I.
=2650+530 = Rs. 3180
Q u e s t i o n : 3
Find the simple interest and the amount when:
Principal = Rs 1500, rate = 12% p.a. and time = 3 years 3 months.
S o l u t i o n :
P = Rs. 1500, R = 12%, T = 3 +
3
12
=
13
4
years
S.I. =
P×R×T
100
=
1500×12×13
100×4
= Rs. 585
Amount=P+S.I.
=1500+585 =Rs . 2085
Q u e s t i o n : 4
Find the simple interest and the amount when:
Principal = Rs 9600, rate = 7
1
2
%
p.a. and time = 5 months.
S o l u t i o n :
P = Rs. 9600R = 7
1
2
% T = 5 months =
5
12
yearsS. I. =
P×R×T
100
=
9600×15×5
100×2×12
= Rs. 300Amount = P + S. I. = 9600 +300 = Rs. 9900
Q u e s t i o n : 5
Find the simple interest and the amount when:
Principal = Rs 5000, rate = 9% p.a. and time = 146 days.
S o l u t i o n :
P = Rs. 5000 , R = 9% , T = 146 days =
146
365
years
S .I . =
P×R×T
100
=
5000×9×146
100×365
=Rs. 180
Amount=P+S .I .
=5000+180 =Rs . 5180
Q u e s t i o n : 6
Find the time when:
Principal = Rs 6400, SI = Rs 1152 and rate = 6% p.a.
S o l u t i o n :
P = Rs. 6400, S. I. = Rs. 1152, R = 6%
T =
S.I.×100
P×R
=
1152×100
6400×6
=
1152
384
= 3 years
Q u e s t i o n : 7
Find the time when:
Principal = Rs 9540, SI = Rs 1908 and rate = 8% p.a.
S o l u t i o n :
P = Rs. 9540 , S. I. = Rs. 1908, R = 8%
T =
S.I.×100
P×R
=
1908×100
9540×8
=
10
4
=2
1
2
years
Q u e s t i o n : 8
Find the time when:
Principal = Rs 5000, amount = Rs 6450 and rate = 12% p.a.
S o l u t i o n :
P = Rs. 5000, A=Rs. 6450, R = 12%
S. I. = A -P
= 6450 -5000
= Rs. 1450
T =
S.I×100
P×R
=
1450×100
5000×12
=
29
12
= 2
5
12
=2 years 5 months
Q u e s t i o n : 9
Find the rate when:
Principal = Rs 8250, SI = Rs 1100 and time = 2 years.
S o l u t i o n :
P = Rs. 8250, S. I. = Rs. 1100, T = 2 years
R=
S.I.×100
P×T
=
1100×100
8250×2
=
1100
165
=6.67%
Q u e s t i o n : 1 0
Find the rate when:
Principal = Rs 5200, SI = Rs 975 and time = 2
1
2
years.
S o l u t i o n :
P= Rs. 5200 , S.I.=Rs. 975 [ T=2
1
2
years=
5
2
years]
R=
S.I.×100
P×T
=
975×100×2
5200×5
=
195
26
=7.5%
Q u e s t i o n : 1 1
Find the rate when:
Principal = Rs 3560, amount = Rs 4521.20 and time = 3 years.
S o l u t i o n :
P = Rs. 3560 , A = Rs. 4521. 20 , T = 3 years
S. I. = A -P = 4521. 20 -3560
= Rs. 961. 20
R =
S.I.×100
P×T
=
961.20×100
3560×3
=
96120×100
100×3560×3
=9%
Q u e s t i o n : 1 2
Shanta borrowed Rs 6000 from the State Bank of India for 3 years 8 months at 12% per annum. What amount will clear off her debt?
S o l u t i o n :
P = Rs 6000, R = 12%, T=3 years 8 months = 3
8
12
=
44
12
years
S.I. =
P×R×T
100
=
6000×12×44
100×12
= Rs 2640
A = P +S. I.
= 6000 +2640
= Rs 8640
Q u e s t i o n : 1 3
Hari borrowed Rs 12600 from a moneylender at 15% per annum simple interest. After 3 years, he paid Rs 7070 and gave a goat to clear off the debt. What is the cost of the goat?
S o l u t i o n :
P = Rs. 12600 R = 15% T = 3 years
S.I.=
P×R×T
100
=
12600×15×3
100
=Rs. 5670
A = Rs. 12600 +Rs. 5670 = Rs. 18270
Hari had to pay Rs. 18270 to the money lender, but he paid Rs. 7070 and a goat.
? Cost of the goat = Rs. 18270 -Rs. 7070
= Rs. 11200
Q u e s t i o n : 1 4
The simple interest on a certain sum for 3 years at 10% per annum is Rs 829.50. Find the sum.
S o l u t i o n :
Let the sum be Rs. P.
S.I. = Rs. 829. 50, T = 3 years, R = 10%
Now, P=
S.I×100
R×T
=
829.50×100
10×3
=
8295
3
= 2765Hence, the sum is Rs. 2765.
Q u e s t i o n : 1 5
A sum when reckoned at 7
1
2
%
per annum amounts to Rs 3920 in 3 years. Find the sum
S o l u t i o n :
Let the required sum be Rs. x.
A = Rs. 3920, R = 7
1
2
%, T = 3 years
Now,
Now, S.I.=
P×R×T
100
=
x×15×3
2×100
=
9x
40
A = P +S. I.
= x +
9x
40
=
40x+9x
40
=
49x
40
But the amount is Rs. 3920.
= >
49x
40
= 3920
= > x =
3920×40
49
=
156800
49
= 3200
Hence, the required sum is Rs. 3200.
Q u e s t i o n : 1 6
A sum of money put at 11% per annum amounts to Rs 4491 in 2 years 3 months. What will it amount to in 3 years at the same rate?
S o l u t i o n :
Given: R=11%, T=2 years 3 months = 2+
3
12
=
27
12
years
Let the required sum be Rs. x.
S.I.=
P×R×T
100
=
x×11×27
9
100×12 4
=
99x
400
A = P +S. I.
= x +
99x
400
=
400x+99x
400
=
499x
400
But the amount is Rs. 4491.
= >
499x
400
= 4491
= > x =
4491×400
499
=
1796400
499
= 3600
Hence, the required sum is Rs. 3600.
? S.I.=
P×R×T
100
=
3600×11×3
100
= Rs. 1188
? Amount=P+S.I.=3600+1188
=Rs. 4788
Q u e s t i o n : 1 7
A sum of money invested at 8% per annum amounts to Rs 12122 in 2 years. What will it amount to in 2 years 8 months at 9% per annum?
S o l u t i o n :
Let the required sum be Rs. x.
S.I.=
P×R×T
100
=
x×8×2
100
=
16x
100
A = P +S. I.
= x +
16x
100
=
100x+16x
100
=
116x
100
But the amount is Rs. 12122.
= >
116x
100
= 12122
= > x =
12122×100
116
= 10450
Now, S.I.=
P×R×T
100
=
10450×9
3
×32
8
100×12 4 1 = Rs. 2508
? A=P+S.I.
= Rs. 10450 + Rs. 2508
= Rs. 12958
Q u e s t i o n : 1 8
At what rate per cent per annum will Rs 3600 amount to Rs 4734 in 3
1
2
years?
S o l u t i o n :
P = Rs. 3600 A = Rs. 4734 T= 3
1
2
=
7
2
years
S. I. = A -P
= 4734 -3600
= Rs. 1134
R=
S.I.×100
P×T
=
1134×100×2
3600×7
=9%
Q u e s t i o n : 1 9
If Rs 640 amounts to Rs 768 in 2 years 6 months, what will Rs 850 amount to in 3 years at the same rate per cent per annum?
S o l u t i o n :
P = Rs. 640, A = Rs. 768, T=2 years 6 months =
5
2
years
S. I. = A -P
= 768 -640
= Rs. 128
R=
S.I.×100
P×T
=
128×100×2
640×5
=8%
P = Rs. 850, R = 8%, T = 3 years
? S.I. =
P×R×T
100
=
850×8×3
100
=
2040
10
=Rs. 204
? A = P +S. I.
= 850 +204
= Rs. 1054
Q u e s t i o n : 2 0
In what time will Rs 5600 amount to Rs 6720 at 8% per annum?
S o l u t i o n :
P = Rs. 5600, A = Rs. 6720, R = 8%
S. I. = A -P
= 6720 -5600
= Rs. 1120
T=
S.I.×100
P×R
=
1120×100
5600×8
=
1120
448
=2
1
2
years
Q u e s t i o n : 2 1
A sum of money becomes
8
5
of itself in 5 years at a certain rate of simple interest. Find the rate of interest.
S o l u t i o n :
Let the sum be Rs. x .
Amount=
8x
5
? S.I.=A -P=
8x
5
-x
=
3x
5
Let the rate be R%.
S.I.=
P×R×T
100
= >
3x
5
=
x×R×5
1
100 20
= > 3x ×20 = R ×x ×5
= > R =
3×x×20
4
x×5
= 12
Hence, the rate of interest is 12 %.
Q u e s t i o n : 2 2
A sum of money lent at simple interest amounts to Rs 783 in 2 years and to Rs 837 in 3 years. Find the sum and the rate per cent per annum.
S o l u t i o n :
Amount in 3 years = (Principal + S. I. for 3 years) = Rs. 837
Amount in 2 years = (Principal + S. I. for 2 years) = Rs. 783
On subtracting:
S. I. for 1 year = (837 -783) = Rs. 54
S. I. for 2 years=
54
1
×2 = Rs. 108
? Sum = Amount for 2 years -S. I. for 2 years
= 783 -108
= Rs. 675
P = Rs. 675, S. I. = Rs. 108 and T = 2 years
R =
S.I.×100
P×T
=
108×100
50 2
675 27 ×2 1
= 8%
Q u e s t i o n : 2 3
A sum of money lent at simple interest amount to Rs 4745 in 3 years and to Rs 5475 in 5 years. Find the sum and the rate per cent per annum.
S o l u t i o n :
Amount in 5 years = (Principal + S. I. for 5 years) = Rs. 5475
Amount in 3 years = (Principal + S. I. for 3 years) = Rs. 4745
On subtracting:
S. I. for 2 years = (5475 -4745) = Rs. 730
S. I. for 3 years=
730
2
×3 = Rs. 1095
? Sum = Amount for 3 years -S. I. for 3 years
= 4745 -1095
= Rs. 3650
P=Rs. 3650, S.I.=Rs. 1095, T=3 years
R=
S.I.×100
P×T
=
1095×100
3650×3
= 10%
Q u e s t i o n : 2 4
Divide Rs 3000 into two parts such that the simple interest on the first part for 4 years at 8% per annum is equal to the simple interest on the second part for 2 years at 9% per annum.
S o l u t i o n :
( )
( )
Let the first part be Rs. x.
Second part = (3000 -x)
? S. I. on x at 8% per annum for 4 years =
x×8×4
2 1
100 50 25 =
8x
25
S. I. on (3000 -x) at 9% per annum =
3000-x ×9×2
1
100 50
=
27000-9x
50
?
8x
25
=
27000-9x
50
= > 8x =
27000-9x ×25
1
50 2
= > 16x = 27000 -9x
= > 16x +9x = 27000
= > x =
27000
1080
25 1
= 1080
? First part = Rs.1080
Second part = (3000 -1080) = Rs. 1920
Q u e s t i o n : 2 5
Divide Rs 3600 into two parts such that if one part be lent at 9% per annum and the other at 10% per annum, the total annum income is Rs 333.
S o l u t i o n :
Let the first part be Rs. x.
Second part = (3600 -x)
? S. I. on x at 9% per annum for 1 years =
x×9×1
100
=
9x
100
And, S. I. on (3600 -x) at 10% per annum =
3600-x ×1×10
1
100
=
3600-x
10
?
9x
100
+
3600-x
10
= 333
= >
9x+36000-10x
100
= 333
= > -x +36000 = 33300
= > -x = 33300 -36000
= > -x = -2700
= > x = 2700
First part = Rs. 2700
Second part = (3600 -2700) = Rs. 900
Q u e s t i o n : 2 6
Mark
? against the correct answer
The simple interest on Rs 6250 at 4% per annum for 6 months is
a
Rs 125
b
Rs 150
c
Rs 175
d
Rs 135
S o l u t i o n :
(a) Rs. 125Principal = Rs. 6250
Simple Interest = 4% per annum
Time = 6 months =
1
2
years
Simple Interest=
P×R×T
100
Simple Interest=
6250×4×1
100×2
Simple Interest=
250
2
= Rs. 125
Q u e s t i o n : 2 7
Mark
? against the correct answer
A sum amounts to Rs 3605 in 219 days at 5% per annum. The sum is
a
Rs 3250
b
Rs 3500
c
Rs 3400
d
Rs 3550
S o l u t i o n :
b
Rs.3500
Amount =Rs. 3605
Time =
219
365
days=
219
365
days
Rate=5% per ? annum
Amount = Sum +
Sum×Rate×Time
100
Amount = Sum (1+
Rate×Time
100
)
Sum=
3605
1+
5
100
×
219
365
=
3605×36500
37595
Sum= Rs. 3500
( )
( )
( )
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