SIMPLE INTEREST SOLUTION - EXAMPURA

[Pages:24]SIMPLE INTEREST SOLUTION

1. (b) Rate (nj) % = 4%

Simple Interest

(lk/kj.k C;kt)= Rs. 150 Time (le;) = 6 months (ekg)

Amount 7

Principal 6

+1

=

6 12

=1 2

year

Let the principal

(ewy/u)= Rs. P

Required Rate% =

1 ?100 = 5 5 %

63

9

We know (ge tkurs gS,a)

3. (d) Note SI for every year will be same.

2.

SI = P ? R ? T 100

uksV% izR;sd o"kZ ds fy, lk/kj.k C;kt cjkcj gksxkA

Simple Interest for 3 years

(3 o"kks? dk lk/kj.k C=;k3t?) 5 = 15%

T Where (tgk?),

Simple Interest for 4 years

SI Simple Interest (lk/kj.k C;kt)

(4 o"kks? dk lk/kj.k C=;k4t?) 5 = 20%

A E P Principal (ewy/u)

Difference in interest (C;kt dk varj)

T R Rate (nj)

G U T Time (le;) A IT P?4?1

T 150 = 2 ?100

= (20 ? 15) = 5% According to question 5% of sum = 42

(iz'ukuqlk, j)

42 Sum = 5 ?100 = Rs. 840

H S 150?200

T IN P=

4

= Rs. 7500

4. (c) Let the rate of interest for two different sources is r 1 and r 2 respectively.

(a) Let principal (ekuk fd ewy/u=) 6P,

ekuk fd nks vyx&vyx lzksrksa ls C;kt nrj1?e'k%

A Hence, Amount

(feJ/u) = 6P ?

7 6 = 7P

vkSrj2 gSA

According to the question

(iz'ukuqlk, j)

H SI = 7P ? 6P = P T Time (le;) = 3 years (o"kZ)

1500?r ?13 100

?

1500?r ?2 3 100

= 13.50

SI = P ? R ? T 100

4500 r 1 ? 4500 r 2 = 1350 1350

(r1 ? r 2) = 4500 = 0.3%

6P?R?3 P = 100

Hence, Required difference in rates

(njksa dk vHkh"V=v0a.r3j%)

R=

100 18

=50 9

= 5 5% 9

Alternate:Note: In such type of questions to save

Alternate:- / oSdfYid fof/:Let the difference in rates (ekuk fd njksa dk varj) = d% According to the question (iz'ukuqlk, j)

your valuable time try to think like that.

uksVbl%izdkj ds iz'uksa esa uhps nh x;h fof/ ds vuqlkj

d =

13.50 1500

?100 3

=1350 4500

lkspus dk iz;kl djsaA

5. (a) Let the sum lent at 8% is

= 0.3% x then

sum lent at 10% is (10000 ?

x)

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ekuk fd 8? C;kt nj ij x #i;s dtZ fn;k x;k rFkk 10% nj ij (10000 ? x) #i;s dk dtZ fn;k x;kA According to the question (iz'ukuqlk, j)

8

10

x ? 100 ? 1 + (10000 ? x) ? 100 ? 1

5 units = Rs. 10,000

1 unit = Rs. 2,000

Hence amount invested at 8%

(8? dh nj

ij fuos'k dh x;h jkf'k=) 2 units (;wfuV)

= 2 ? 2000 = Rs. 4000

Amount invested at 10% (10? dh nj ij

9.2 = 10000 ? 100 ? 1

fuos'k dh x;h jkf'=k)3 units (;wfuV)

= 3 ? 2000 = Rs. 6000

6. (c) Time = 2 years 3 months

8 x +10(10000? )x

100

100

= 920

8 x + 100000 ? 10 x = 92000

= 2 +

3 =9 12 4

years

?2 x + 100000 = 92000 ?2 x = 92000 ? 100000 ?2 x = ? 8000

SI = P ? R ? T

We know

100

T x = 4000

Hence, Amount lent at ( 8% C;kt nj ij dtZ

A E nh x;h jkf'k8)% = Rs. 4000

T Amount lent at (10? C;kt nj ij dtZ nh x;h

G U jkf'k)10% = (10000 ? 4000)

P = Rs. 1600, T =

9 4 years, SI = Rs. 252

Put values in the above formula

fof/ esa eku j[kus ,ij)

(mijksDr

A IT = Rs. 6000

Alternate:-/ oSdfYid fof/:-

1600?R?9 252 = 4?100

T Note:- In such type questions to save

252 = 36 R

H S your valuable time follow the given below

method.

T IN uksVb%l izdkj ds iz'uksa esas vius cgqewY; le; ds

252 R = 36 = 7%

cpr ds fy, vki uhps nh x;h fof/ dk iz;ksx dj 7.

A ldrs gSaA

By alligation Method (feJ.k fu;e ds }kjk)

(b) Let the principal

(ekuk fd ewy/u=) 9 units

Hence simple interest

TH (lk/kj.k C;kt)=

4 9 ?9 = 4 units

(i)

Ist part

IInd part

Let, Rate of interest (C;kt nj) = R%

8%

10%

R = T (Given)

By using formula,

9.2%

SI = P ? R ? T 100

Ratio of

0.8

quantity

2

1.2

:

3

9?R?R

400

4 = 100 R2 = 9

R =

20 3

= 6 2% 3

According to the question (2 + 3) units = Rs. 10,000

8. (c) Principal = Rs. 400,

(iz'ukuqlk, j)

Amount = Rs. 480

Simple Interest = Rs. (480 ? 400)

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= Rs. 80 Time = 4 years

=

2 ?100 5 10

= 4%

Rate% =

SI ? 100 P ? T

Rate% =

80?100 400?4

=8000 1600

= 5%

10. (c) Principal

Interest

5

2

+

2 5

New rate of interest = (5 + 2) = 7%

Required time =

2 ?100 58

= 5 years

400?7?4

Interest =

100 = 112

11. (a) Principal (ewy/u)= Rs. 1750

9.

Hence amount = Rs. (400 + 112)

= Rs. 512

Alternate:-

Note:- In such type of questions to save

T your valuable time follow the given below

method.

A E uksVb%l&izdkj ds iz'uksa esas vius cgqewY; le; ds

T cpr ds fy, vki uhps nh x;h fof/ dk iz;ksx dj

G U ldrs gSaA

A IT Increased in rates (nj esa o`f=?4 ? 2 = 8%

Hence increased in amount

(feJ/u esa o`f?)

T 8

H S = 400 ? 100 = 32 T IN Hence new amount

(u;k feJ/u)

Rs. (480 + 32) = Rs. 512

(a) Let principal

A (ekuk fd ewy/u=) 5 units

H Hence interest = 5 ? T Time = 10 years,

2 5 = 2 units

Let the first part (ekuk fd igyk Hkk=xx) Hence second part (blfy, nwljk Hkkx)

= (1750 ? x)

According to the question (iz'ukuqlk, j)

8

6

x ? 100 ? 1 = (1750 ? x) ? 100 ? 1

4 x = 5250 ? 3 x 7 x = 5250 x = 750

First part (igyk Hkkx=)Rs. 750

Second part (nwljk Hkkx)

= Rs. (1750 ? 750) = Rs. 1000 Required interest

(vHkh"V C;kt)

8 = 750 ? 100 = Rs. 60

Alternate:Note:- In such type of questions to save your valuable time follow the given below method.

By using formula,

uksVb%l&izdkj ds iz'uksa esa vius cgqewY; le; ds

Rate% =

2 ?100 5 10

= 4%

cpr ds fy, vki uhps nh x;h fof/ dk iz;ksx dj ldrs gSaA

Alternate:-

Let, Principal (ekuk fd ewy/u=) 100

Note:- In such type of questions to save your valuable time follow the given below method.

usits in both cases (nksuksa fLFkfr;ksa esa)

Ist part

II nd part

Total

uksVb%l&izdkj ds iz'uksa esa vius cgqewY; leP;ridnscipal 100 ?3 :

100

+ ?4

700 units

cpr ds fy, vki uhps nh x;h fof/ dk iz;ksx dj Interest 8 ?3 : 6 ?4

ldrs gSaA

Note: Interest is same in both cases

(nksuksa

Principal

Interest

fLFkfr;ksa esas C;kt cjkcj gksxkA)

5

2

+

2 5

According to the question 700 units = Rs. 1750

(iz'ukuqlk, j)

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1750 1 unit = Rs. 700

Ist part 4%

IIn d part 5%

1750 24 units = Rs. 700 ? 24 = Rs. 60

4.4 %

Hence, required interest (vHkh"V C;kt)

= Rs. 60

0.6

:

0.4

Ratio of

12. (d) Avg. rate of interest (vkSlr C;kt nj)

amounts

3

:

2

Hence Required Ratio (vHkh"V vuqikr)

300 = 1550

?100 3

=200 31

%

=3: 2

14. (b) Time (le;) = 4 years (o"kZ)

By using mixture and Alligation Rule

Let sum = 5 units

(feJ.k fu;e ds }kjk,)

Ist part

T 5%

IInd part 8%

Hence interest = 5 ?

1 5 = 1 unit

Required rate% =

1 100 5 ? 4 = 5%

A E 200 G UT 31

%

15. (a)

Amount (Rs.) 520

Time (years)

5

A IT Note: Always remember to solve such

T type of questions multiply by 31 in both

+48 568

+2 7

H S parts.

Hence interest in 2 years = Rs. 48

uksVb%l izdkj ds iz'uksa dk gy djrs gq, ges'kk nksuksa

T IN Hkkx 31 ls xq.kk djsaA

Interest in 1 years = Rs.

48 2 = Rs. 24

A Ist part H 155%

IInd part 248%

Interest in 5 years = Rs. 24 ? 5 = Rs. 120 We know,

SI = Amount ? Principal

T Principal = Rs. (520 ? 120) = Rs. 400

200 %

16. (c) Let the latter amount = Rs.

x

According to the question,

48

45

Ratio of

amounts 16

15

Required Ratio (vHkh"V vuqi=k1r)6 : 15 13. (b) Avg. rate of interest (vkSlr C;kt nj)

500?12?4 + ?x10?4

100

100

4x 240 + 10 = 480

4x 10 = 240

=

440 5000

?100 2

= 4.4%

x = 600 Hence latter amount =

Rs. 600

By using mixture and alligation rule

Alternate:-

(feJ.k fu;e ds }kjk,)

Note: In such type of questions to save

your valuable time follow the given below

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method.

uksVb%l&izdkj ds iz'uksa esa vius cgqewY; le; ds cpr ds fy, vki uhps nh x;h fof/ dk iz;ksx dj ldrs gSaA Interest on first part (igys Hkkx ij C;kt)

28 = 2500 ? 100 = Rs. 700 Remaining S.I. that is received from C

( C ls izkIr 'ks"k lk/kj.k C;kt)

= Rs. 1120 ? Rs. 700 = Rs. 420

500?12?4 = 100 = Rs. 240

Principal

(ewy/u)= 420 ?

100 28 = Rs. 1500

Remaining interest ('ks"k C;k=t)Rs. (480

? 240) = Rs. 240

19. (d)

Amount

Time

Hence Required amount (vHkh"V feJ/u)

(Rs.)

(years)

756

2

17.

240 = (4?10) ?100 = Rs. 600

(c) Let initial capital

T = 100 units 100

(ek=kk fd vkjafHkd laif?k)

A TE 8%

31 4

%

AGITU 8%

1

4

31 4

H ST difference T IN According to the question

(iz'ukuqlk, j) 20.

1 4 unit = Rs. 61.50

A 1 unit = Rs. 61.50 ? 4 = Rs. 246

100 units = Rs. 24600

H Hence, Required capital (vHkh"V laif?k)

T = Rs. 24600

+117 873

Hence interest

1.5 years

3

1 2

in

1

1 2

years

= Rs. 117

Interest in 1 year =

117 3 ? 2 = Rs. 78

Interest in 2 years = Rs. 78 ? 2 = Rs. 156 Principal = Rs. (756 ? 156) = Rs. 600

Required rate % =

78 600 ?100 = 13%

(c) Amount = Rs. 7000 Total interest in 5 years

10

50

1

= 5? 3 % = 3 % = 6

Principal 6

Amount (6 + 1)

Alternate:-

?1000

?1000

Difference in percentage (? esa varj)

6000

7000

31 = 8% ? 4 %

Hence Required principal = 21. (a) Time = 4 years

Rs. 6000

1 4 % = 61.50

100% = 24600 18. (d) Let sum lent to c = Rs. x

Sum

Amount

40

41

+1 unit

According to the question (iz'ukuqlk, j) Total interest of 4 years (4 o"kks? dk dqy C;kt)= 4 ? 7% = 28% S.I. received from B ( B ls izkIr lk/kj.k C;kt) 22

Required rate% =

1 ?100 40 1

? 4 =

10%

(d) Let the sum = Rs. P, T

8 1 = 12 yrs,

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15 T2 = 12 years

55.50

100 units =

1.5 ? 100 = Rs. 3700

According to the question,

24. (c) same as question no. 5 we will use the

P?5?15 ? P?4?8 100 ?12 100 ?12

= 129

alligation method (iz'u la[;k 5 dh rjg ge

;gk? Hkh feJ.k fu;e dk iz;ksx djsaxs)

6%

10%

43P

1200

= 129

P = Rs. 3600 Hence required sum

(vHkh"V ;ksx)

9.2 %

= Rs. 3600

0.8 : 3.2

Alternate:-

Let sum (ekuk fd ;ksx=) 100 units

According to the question,

T 100

(8?4)%

(15?5)%

GA TE 32

75

A ITU 43 units

1

:

Parts are

4

1000

1000

(4+1) ?4, (4+1) ?1

800, 200 25. (d) Total interest paid in 3 years

(3 o"kks? esa dqy

C;kt dk Hkqxr=ku12) ? 3 = 36%

Interest (C;kt) = Rs. 5400

According to the questions (iz'ukuqlk, j)

36% of sum = Rs. 5400

H ST difference

43 units = Rs. 129

T IN 1 unit = Rs. 3

100 units = Rs. 3 ? 100 = Rs. 300

A yearly sum = Rs. 12 ? 300 = Rs. 3600

Note:- Time is given in months and

rate% is given per annum. Hence we

26.

H multiplied the answer by 12.

T uksVl%e;&ekg esa fn;k x;k gS vkSj nj izfr'kr okf"kd

5400

1% of sum = Rs.

36

5400 sum = 36 ?100 = Rs. 15000

Hence, required sum (vHkh"V ;ksx)

= Rs. 15000

(c) Amount (Rs.)

Time (years)

gS blfy, geus m?kj dks 12 ls xq.kk dj fn;k gSA

1012

+55.20

23. (a) Let the sum = 100 units

21

2

+1

1 2

years

100

1067.20

4

11.5%

10%

Interest

in

3 2

years = Rs. 55.20

11.5

10

3 Interest in 2 years = Rs. 55.20

Interest in 1 year (1 o"kZ esa C;kt)

1.5 According to the question, 1.5 units = 55.50

55.50 1 units = 1.5

55.20 = 3 ? 2 = Rs. 36.80

Interest in 4 years (4 o"kks? esa C;kt)

= 36.80 ? 4 = Rs. 147.2 Principal = Amount ? Interest

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= 1067.20 ? 147.20 = Rs. 920

36.80

Required Rate% =

920 ?100 = 4%

27. (a)

Amount (Rs.)

720 +300

1020

Time (years)

2 +3

5

25?R?R 16 = 100 R2 = 64

R = 8% 31. (a) Let the principal

= 100 units

(ekuk fd ewy/u)

100

10%

12

1 2

%

gain

Interest in 3 years = Rs. 300

10

12.5

28. 29.

Interest in 1 years = Rs. 100

Interest in 2 years = Rs. 100 ? 2 =

Rs. 200

Required Sum = 720 ? 200 =

Rs. 520

T (d) Number of days in a years

(1 o"kZ esa fnuksa dh=l3a6[5;k)

A E Total money (dqy #i;s)= 1 ? 365

T = Rs. 365

G Time = 1 year,

U Rate% = 5%

A IT 365?100

T Sum =

5?1 = Rs. 7300

H S (d) Let the amount invested (ekuk fd fuos'k dh

T IN x;h jkf'k)= Rs. P

According to the question,

A P?9?2 +P?10?2 100 100

= 760

H (18P+20P)

32.

100

= 760

T 38P = 76000, P = 2000

Alternate:-

+2.5

According to the question, 2.5 units = Rs. 1250

1250 1 unit = Rs. 2.5 = Rs. 500

100 units = Rs. 500 ? 100 = Rs. 50,000

Hence, total principal (dqy ewy/u)

= Rs. 50,000 Alternate:-

1 12 2 % ? 10% = 2.5%

2.5% = 1250 (given) 100% = 50000

(c) T1 = 15 months =

15 12 years,

1

15

R1 = 7 2 % = 2 %

Total interest percent (dqy C;kt nj)

= (9 ? 2)% + (10 ? 2)%

8 T2 = 8 months = 12 years,

38% = 760

100% = 2000 Hence required principal = Rs. 2000

1

25

R2 = 12 2 % = 2 %

30. (a) Let sum = 25 units

Let the principal = P

Sum

Interest

According to the question,

25

16

?

16 25

P?15?15 ? P?25?8 12?2?100 12?2?100

= 32.50

Time(t) = Rate(R%) (Given)

225P ?200P 2400 2400

= 32.50

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25P 2400 = 32.50 P = Rs. 3120

Hence required principal =

Rs. 3120

Ist part 32%

IInd part 40%

33. (a) Sum 72

Amount 81

+9

Ratio of amounts

35 %

5

:3

interest

By using formula,

16000

Required part (vHkh"V H=kk(x5)+ 3) ? 5

34. 35. 36.

Time =

9 ?100?4 72 25

= 2 years

(a) Total days =

T May June July Aug. Sept

21 + 30 + 31 + 31 + 10

A E = 123 days

T By using formula,

G U 7300?5?123 A IT SI = 100?365 = Rs. 123

H ST (c) Gain% =

6

1%?2 4

?

(4

?

2)%

T IN = 12.5% ? 8% = 4.5%

Principa = Rs. 5000

A Required gain = 5000 ?

4.5 100 = Rs. 225

(c) Principal = Rs. 16000, Interest = Rs. 700

H Avg. rate of interest (vkSlr C;kt nj)

T 700

35

= Rs. 10,000 37. (b) Let principal = P,

Amount = 3 P Interest = 3P ? P = 2P According to the question,

P?R?20 2P = 100 R = 10%

Let after t year it will become double

(ekuk fdt o"kZ ds ckn ;g nksxquk gks tk,xk)

Hence, interest = 2P ? P = P

P?10?t P 100 t = 10 years

Alternate:Note: In such type of questions to save your valuable time follow the given below method.

uksVb%l izdkj ds iz'uksa esa vius cgqewY; le; ds cpr ds fy, vki uhps nh x;h fof/ dk iz;ksx dj ldrs gSaA)

= 16000 ?100 = 8 %

Now, By alligation Rule

Ist part

IIn d part

4% ? 8

5% ? 8

(feJ.k fu;e ds }kjk,)

Principal 1

1

Amount

Interest

Time (Years)

3 diff. 2 diff.

2

?

1 2

1

20

?

1 2

10

35 8

% ? 8

Hence required time = 10 years 38. (c) Let the first part = x

Note: To make your calculation easier multipling each part by 8.

second part = (1500 ? x) According to the question,

uksVv%iuh x.kuk dks vklku djus ds fy, izR;sd Hkkx dks 8 ls xq.kk dj nsaA

x ?10?5 =(1500? )x?12.5?4

100

100

50 x = (1500 ? x)50

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