Solution: P = Rs. 6400, R = 6%, Time = 2 years Simple Interest

Chapter 12: Simple Interest

Page no.: 165

Exercise: 12A

Question 1:

Solution: P = Rs. 6400, R = 6%, Time = 2 years

Simple Interest = 6400 6 2

100 100

P R T

= Rs. 768

Amount = principal + Simple interest

= 6400 + 768

= Rs. 7168

Question 2:

Solution: P = Rs. 2650, R = 8%, T = 1

22

years = 5

2years

Simple interest = 100

P R T =

2650 8 5

100 2

= Rs. 530

Amount = Simple interest + P

=2650 + 530

= Rs 3180

Question 3:

Solution: P = Rs. 1500, R = 12%, T = 3

312

= 13

4years

Simple Interest = 100

P R T =

1500 12 13

100 4

= Rs. 585


= 1500 + 585 = Rs. 2085

Question 4:

Solution: P = Rs. 9600, R = 1

72

%, = 15

2% T = 5 month or

5

12years


P R T =

9600 15 5

100 2 12

= Rs. 300


= 9600 + 300 = Rs. 9900

Question 5:

Solution: P = Rs. 5000, R = 9%, T = 146 days or 146

365years

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P R T =

5000 9 146

100 365

= Rs. 180


= 5000 + 180 = Rs. 5180

Question 6:

Solution: P = Rs. 6400, R = 6%, Simple Interest = Rs. 1152

Time = 100SI

P R

=

1152 100

6400 6

= 1152

384= 3 years

Question 7:

Solution: P = Rs. 9540, R = 8%, Simple Interest = Rs. 1908

Time = 100SI

P R

=

1908 100

9540 8

= 10

4=

12

2years

Question 8:

Solution: P = Rs. 5000, R = 12%, Amount = Rs. 6450

Simple interest = Amount - Principal

= 6450 – 5000

= Rs. 1450

Time = 100SI

P R

=

1450 100

5000 12

= 29

12=

52

12 years

Question 9:

Solution: P = Rs. 8250, Simple interest = 1100, Time = 2 years

R = 100 1100 100

8250 2

SI

P T

= 1100

6.67%165

Question 10:

Solution: P = Rs. 5200, S.I. = Rs. 975, T = 1

22

years = 5

2years

R = 100 975 100 2

5200 5

SI

P T

= 195

26%

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Question 11:

Solution: P = Rs. 3560, A = 4521.20, T = 3 years

Simple interest = Amount – Principal

= 4521.20 – 3560

= Rs. 961.20

Rate = 100 961.20 100

3560 3

SI

P T

= 9%

Question 12:

Solution: P = Rs. 6000, R = 12%, T = 3 years 8 months = 8

312

= 44

12 years


P R T =

6000 12 44

100 12

= Rs. 2640

Amount = Principal + Simple interest

= 6000 + 2640

= Rs. 8640

Question 13:

Solution: P = Rs. 12600, R = 15%, T = 3 years

S.I. = 100

P R T =

12600 15 3

100

= Rs. 5670

A = 12600 + 5670

= Rs. 18270

Hari had to pay Rs. 18270 to the money lender, but he paid Rs. 7070 and goat.

Cost of the goat = 18270 – 7070

= Rs. 11200

Question 14:

Solution: Let the sum be Rs. P

Simple interest = Rs. 829.50, T = 3 years, R = 10%

P = 100 829.50 100

10 3

SI

R T

= 8295

3= Rs. 2765

Question 15:

Solution: Let the required sum be Rs. x.

A = Rs. 3920, R = 1

72

%, T = 3 year

Simple interest = 15 3

100 2 100

P R T x

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= 9

40

x

Amount = P + S.I.

=9 40 9

40 40

x x xx

= 49

40

x

But the amount is Rs. 3920.

49

40

x= 3920

x = 3920 40 156800

49 49

= Rs. 3200

Hence, the required sum is Rs. 3200

Question 16:

Solution: Given: R = 11%, T = 2 years 3 months = 3 27

212 12

years

Let the required sum be Rs. x

S.I. = 100

P R T =

11 27 99

100 12 400

x x

A = P + S.I.

A = 99 400 99 499

400 400 400

x x x xx


= 499

400

x = 4491

x = 4491 400 1796400

499 499

= 3600


S.I. = 100

P R T =

3600 11 3

100

= Rs. 1188

Amount = P + S.I.

= 3600 + 1188

= Rs. 4788

Question 17:

Solution: Let the required sum be Rs. x

S.I. = 100

P R T =

8 2 16

100 100

x x

A = P + S.I.

= 16 100 16 116

100 100 100

x x x xx

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116

100

x= 12122

x = 12122 100

116

= Rs. 2508

A = P + S.I.

= 10450 + 2508

= Rs. 12958

Question 18:

Solution: P = Rs. 3600, A = Rs. 4734, T = 1 7

32 2 years

S.I. = A – P

= 4734 – 3600

= 1134

R = 100 1134 100 2

3600 7

SI

P T

= 9%

Question 19:

Solution: P = Rs. 640, A = Rs. 768, T = 2 years 6 months = 5

2years

S.I. = A – P

= 768 – 640

= Rs. 128

R = 100 128 100 2

640 5

SI

P T

= 8%

P = Rs. 850, R = 8%, T = 3 years

S.I. = 100

P R T =

850 8 3

100

=

2040

10

= Rs. 204

A = P + S.I.

= 850 + 204

= Rs. 1054

Question 20:

Solution: P = Rs. 5600, A = Rs. 6720, R = 8%

S.I. = A – P

= 6720 – 5600

= Rs. 1120

T = 100 1120 100 1120

5600 8 448

SI

P R

= 1

22

years

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Question 21:

Solution: Let the sum be Rs. X

Amount = 8

5

x

Simple interest = A – P

= 8

5

x - x =

3

5

x

Let the rate be R%

S.I. = 100

P R T

3 5

5 100

x x R

3 20 5x R x

R = 3 20

5

x

x

= 12

Hence, the rate of interest is 12%

Question 22:

Solution: 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

( 2)1 = 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 = 100 108 100

675 2

SI

P T

= 8%

Question 23:

Solution: 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

32

= 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 = 100 1095 100

3650 3

SI

P T

= 10%

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Question 24:

Solution: Let the first part be Rs. X

Second part = (3000 – x)

S.I. on x at 8% per annum for 4 years = 8 4 8

100 25

x x

S.I. on (3000 – x) at 9% per annum = (3000 ) 9 2

100

x

= 27000 9

50

x

8 27000 9

25 50

(27000 9 ) 258

50

16 27000 9

16 9 27000

270001080

25

x x

xx

x x

x x

x

First part = Rs. 1080

Second part = (3000 – 1080) = Rs. 1920

Question 25:

Solution: Let the first part be Rs. x.

Second part = (3600 – x)

S.I. on x at 9% per annum for 1 year = 9 1 9

100 100

x x

And S.I. on (3600 – x) at 10% per annum = (3600 ) 1 10 3600

100 10

x x

9 3600333

100 10

9 36000 10333

100

x x

x x

-x + 36000 = 33300

-x = 33300 – 36000

-x = - 2700

x = 2700

First part = Rs. 2700

Second part = (3600 – 2700) = Rs. 900

Exercise: 12B

Page no.: 166

Question 1:

Solution: (a) Rs. 125

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Principal = Rs. 6250

Rate of interest = 4% per annum

Time = 6 months = 1

2 year


P R T

= 6250 4 1 250

100 2 2

= Rs. 125

Question 2:

Solution: (b) Rs. 3500

Amount = Rs. 3605

Time = 219

365days

Rate = 5 % per annum

Amount = sum + 100

sum rate time

= sum (1 )100

rate time

Sum = 3605 3605 36500

5 219 375951

100 365

= Rs. 3500

Question 3:

Solution: (c) 8%

Let the sum be Rs. X.

Rate of interest = R%

Time = 1 5

22 2

years

Amount = 6

5Sum

Rate = ?

Principal + S.I. = Amount

Principal + Principal Rate Time 6

Principal100 5

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5 6

100 2 5

5 6(1 )

100 2 5

61

40 5

140

5

xRx x

rx x

r

r

R = 8%

Question 4:

Solution: (b) 9 months

Let the time be T years.

Principal = Rs. 8000

Amount = Rs. 8360

Rate = 6% per annum

Amount = Principal (1 )100

Rate Time

8360 6

18000 100

T

8360 6

18000 100

T

T = 8360 8000 100

( )8000 6

= 360 100

8000 6 =

612

8 months

= 9 months

Question 5:

Solution: (b) 10%

Let the sum be Rs. X and the rate be r%

According to question

Amount = 2x

P + S.I. = 2x

P + 100

P R T = 2x

X 10

(1 )100

R = 2x

100 10

100

r= 2

10 r = 200 – 100

10 r = 100

R = 100

10= 10 %

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Question 6:

Solution 6: (c) Rs. 100

x

Simple interest = Rs. x

Rate = x% per annum

Time = x years

Simple interest = Principal Rate Time

100

x = Principal

100

x x

Principal = Rs. 100

x

Question 7:

Solution: (b) 8%

Time = 5 years

Simple interest = 2

5P

2

100 5

5 2

100 5

2 100

5 5

P R TP

R

Rate

Rate = 8%

Question 8:

Solution: (c) 22 years

1R = 12%

2R = 10%

1P = Rs. 8000

1P = Rs. 9100

Let their amount S be equal in T years.

1Amount = 1. .S I + 1P

= 1 1

100

P R T + 1P

= 8000 12

100

T + 8000

2Amount = 2 2. .S I P

= 2 2

100

P R T + 9100

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= 9100 10

100

T + 9100

= 910 T + 9100

1Amount = 2Amount

960T + 8000 = 910T + 9100

960T – 910T = 9100 – 8000

50T = 1100

T = 22

Hence, after 22 years their amounts will be equal

Question 9:

Solution: (c) Rs. 768

Let the rate be R%

S.I. = A – P

= 720 – 600 = Rs. 120

Time = 4 years

R = 100 100 120

600 4

SI

P T

= 5%

Rate of interest = 5%

Now, R = (5 + 2) % = 7%

S.I. = 600 7 4

100 100

P R T

= Rs. 168

Amount = S.I. + P

= 600 + 168 = Rs. 768

Question 10:

Solution: (d) 2y zx

y = S.I. on x = 100

x R T ……………….. (i)

z = S.I. on y= 100

y R T ………………… (ii)

Dividing equation (i) by (ii):

2

100( )

100

y x R T

z y R T

y x

z y

y xz

Question 11:

Solution: (a) 1

14

years

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Rate = 10% per annum

Simple Interest = 0.125 X Principal

100

P R T = 0.125 X Principal

100

T= 0.125

T = 1.25 = 1

14

years

Question 12:

Solution: (b) Rs. 2400

Rate = 3

3 %4

= 15

%4

per annum

Time = 1

23

= 7

3years

S.I. =

15 7

4 3

100

P

P = 210 100

15 7( )

4 3

= 600 X 4

P = Rs. 2400

Test Paper

Page no.: 168

Question 1:

Solution: P = Rs. 6300, R = 8%, T = 8

12years

S.I. = 6300 8 8

100 100 12

P R T

= Rs. 336

Question 2:

Solution: Let the sum be Rs. x.

S.I. = 10 2

100 100 5

P R T x x

Now, A = P + S.I.

A = 6

5 5

x xx

But the amount is Rs. 6600

6

66005

x

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x = 6600 5

55006


Question 3:

Solution: P = Rs.3625, A = Rs. 4495, T = 2 years

S.I. = A – P

= 4495 – 3625

= Rs. 870

S.I. = 100

P R T

870 = 3625 2

100

R

R = 870 100 87000

3645 2 7250

R = 12%

Question 4:

Solution: P = Rs. 3600, A = Rs. 4410, R = 9%

S.I. = A – P

= 4410 – 3600

= Rs. 810

T = . . 100 810 100

3600 9

S I

P R

T = 90 1

236 2

years

Question 5:

Solution: Let the sum be Rs. x

Amount = Rs. 2x

S.I. = (2x – x) = Rs. x

Time = 12 years

P = x , S.I. = x , T = 12 years

R = 100 . . 100

12

S I x

P T x

R = 8.3%

Question 6:

Solution: Let the sum be Rs. x.

Amount = 4

3x

S.I. = A – P

= 4

3x x =

3

x

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Let the rate be R%

S.I. = 100

P R T

3

x=

6

100

x R

R = 100 100

6 3 18

x

x

R = 5.55%

Question 7:

Solution: (c) 9%

Let the sum be Rs. x.

A = 49

40

x

We know:

A = P + S.I.

S.I. = A – P

= 49

( )40

xx =

9

40

x

Let the rate be R% per annum.

S.I. = 100

P R T

9

40

x=

5

100 2

x R

R = 9 20 2

40

R = 9%

Question 8:

Solution: (c) 3500

A = Rs. 3626, R = 6%, T = 216 days= 216

365years

Let the required sum be Rs. x.

S.I. = 6 219

100 100 365

P R T x

= 1314

36500

x

A = P + S.I.

= x + 1314

36500

x

= 36500 1314 37814

36500 36500

x x x


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37814

36500

x = 3626

x = 3626 36500

37814

= 3500

The required sum is Rs. 3500

Question 9:

Solution: (a) 9 months

P = Rs. 6000, A = Rs. 6360, R = 8%

S.I. = A – P

= 6360 – 6000 = Rs. 360

S.I. = . . 100 360 100

6000 8

S I

P T

= 6

8 years

= 6

8× 12 months

= 72

8= 9 months

Question 10:

Solution: (c) 12%


S.I. = Rs. 3

5

x

Let the rate be R% per annum.

S.I. = 5

100 100 20

P R T x R Rx

3

5 20

x Rx

R = 3 20

5

x

x

= 12%

Question 11:

Solution: (d) Rs. 100

x

Let the sum be Rs. P

Time = x years

Rate of interest = x % per annum

S.I. = Rs. x

S.I. = 100

P R T

x = 100

P x x

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P = 100x

x x

= Rs.

100

x

Question 12:

Solution: (b) 10%


Amount = Rs. 2x

Time = 10 years

S.I. = A – P

= 2x – x = Rs. x

S.I. = 100

P R T

X = 10

100

x R

R = 100

10

x

x

= 10%

Fill in the blanks.

Question 13:

Solution: P = 100 . .S I

R T

(ii)

Solution: R = 100 . .S I

P T

(iii)

Solution: 10%


Amount = Rs. 2x

S.I. = A – P

= 2x – x = Rs. x

Let the rate of interest be R%

Time = 10 years

S.I. = 100

P R T

x = 10

100

x R

R = 10%

(iv)

Solution: 8%


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Amount = Rs. 6

5x

S.I. = A – P

= 6

5x - x = Rs.

5

x

Let the rate of interest be R%.

Time = 2.5 years

S.I. = 100

P R T

5

x =

2.5

100

x R

R = 100

2.5 5= 8%

Question 14:

(i)

Solution: False

S.I. = 100

P R T

X = 100

x R x

R = 100 x

x x

R = 100

x%

(ii)

Solution: True

(iii)

Solution: True

Let the sum be Rs. X

S.I. = 100

P R T

S.I. = 10 10

100

x

S.I. = Rs. X

Amount = S.I. + P

= x + x = Rs. 2x

(iv)

Solution: True

P = Rs. 1000 , R = 5%, T = 73 days= 73

365years

S.I. = 100

P R T =

1000 5 73

100 365

S.I. = Rs. 10

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Documents

Solution: P = Rs. 6400, R = 6%, Time = 2 years Simple Interest