Tnpsc Maths1

7/21/2019 Tnpsc Maths1

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TNPSC MATHS. R.SIVA M.Sc.,B.Ed., Cell : 8015118094 mail id : [email protected]

For Full materials contact Cell 8015118094 Page 1

www .tnpsctamil.in{ -} { t t ~ ~y

.TNPSC z~ { (

Aptitude and Mental Ability ) } tz

~ t

~y. {~ } u .

{ . Aptitude and

Mental Ability {~

8015118094 . { ~} [email protected] .

| u . }

z www .tnpsctamil.in { t }{

{t} . Percentage

Highest Common Factor (HCF)

Lowest Common Multiple (LCM)

Ratio and Proportion

Simple interest

Compound interest

Area

Volume Time and Work

~

t

{ u

z ~

t |

1 = 24

1 = 7

1 z = 12 u

1 z = 365 y

1 ~ z = 366 y

10 z = 1 {z

100 z = 1 z

1000 z = 1 1 = 60

1 = 60 u = 60 x 60 = 3600

1 = 24 = 1440 u ( 24 x 60 )

www.tnpsctamil.in 1 of 51.


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1 = 86 , 400 ( 24 x 60 x 60 )

60 = 1

1 =

60 u = 1

1 = u 60 t z

120 u

120 = 120 x = 2 u

u 60 t z

u 60 t z

360 u

360 u = 360 x = 6

u 60 t z

3 45 u u 1 = 60 u 3 = 3(60) = 180 u

3 45 u = 180 + 45 = 225 u

3600

5400

5400 = 5400 x = = 1 3600 t

12 z 12 .

z 12 12 .

12 12 | } 24

{ 12 t

y z. ~ z.

8.00 . = 8.00

10.25 . = 10.25 + 12 = 22.25

12 z = 12.00

{ 12

~} 12 t t z

23.10 = 23.10 12.00 = 11.10 .

09.20 = 09.20 .24 = 12

t

. 4.00 . 4.00 -

4.00 . = 4 + 12 = 16

= 4.00 . 4.00 .= 16.00 4.00 = 12



3/51



} z } | 22.10 t ~y

02.50 t }| . z

}| = 02.50

} | ~y = 22.10

(} ) = 24.00 22.10 + 2.50 = 1.50 + 2.50 = 4.40

z = 4 40

z} 9.00 t tv }} .

| y y 5.30 t{ }

} y y | }

} y| ~y 9.00 ,

~y { | 12.00 ~y 12.00 9.00 =

3.00

y = 5.30 .

y y | = 3.00+ 5.30 = 8.30

~ z

z 400 z 4 }

~ z

z 365 y

~ z 366 y

y 15 t 27 - y {

y 17 ( 31 14 ) y 15 } 31 | } 14 t

~ 30

t 27

{ 74 y

u 7 t z

298 y = = 42 u 4

{ y 7 t z



4/51





5/51



yt

12 u = 1

660 = 1 u

8 u = 1

10 = 1 }

16 } = 1 z

2000 z = 1 }

y

10 . = 1.

10 .= 1

10 .= 1

10 = 1 10 =1 t

10 t = 1 .

{

10 . = 1.

10 . = 1

10 . = 1

10 = 1 10 =1 t

10 t = 1 .

10 . = 1.

10 . = 1

10 . = 1

10 = 1 10 =1 t

10 t = 1 .

|t 200 . 40 | z ~ t

|t z { y u z

|t 200 .

40 |t = 40 x 200 = 8000 . = 8 y 1000 . = 1

~y 350 . 5 u | {

yt ~



6/51



5 = 5000

5000 350 { 14 100 .

14 y ~ . 100

~

{} } { } ~ {} = 2 ( + )

{} = 4 x t

t{} = } tu}

u t{} = ~t + +

{} = } t }

{} = } t }

{} = } t }

t t{} 2a + 2

y{} P = 2 r y{}P = ( +2) r y{}P = ( +2) r

~

~ t {} } ~

~

{} ~ = x .

A=lb

{} ~ = t x t .

A=a2

u t{}

~= (~t x ) .

A = bh



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t~ = (~t x ) .

A = bh

y{} ~ :A = r2 . r}y{}

y{}~:A = r2 .

y{}~:A = r2. r}y{}

{}~ h (a+b).

a,b }~tu h}

~tut

{} ~A = bh. b}~t h}

tt{}~ A = a2. a}

tt{}t

tt{}~A =h .

a ah

a a

a



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tt{}~A=

. s=

a,b,c }tu

{}~A= d( h1 + h2) .

dy h1, h2}tv

|y{~u{

u

{}~A = ( d1 d2 ) .

d1, d2 }yu

{}~A = bh. b}~t h}

~

}

~ = v{} ~ {} ~

y~

}

~ = y~} ~ y{} ~



9/51



y~}yD0 r vi}

l = 2r

y~}p = l + 2r

y~}yD0 r

y~}~A= r2

}lry~}~A=

l r

t~y{}~~ =ph

p-- y{}v

h--y{}

t~y{}{~~ph + 2A

p-- y{}v , h--y{} ,

A y{}~~

t~y{} =Ahh--y{} ,A y{}~~

{}t~2h( l+ b)

l bh

{}t~ = 4 a2

{}{~ = 2 ( lb + bh + lh) {}{~ = 6a

2

{} = l b h {} V = a

3

l , h, r

-

l

2= h

2+ r

2

}~ = y~}~

rl = r2

-

z} = ty~~

tt~

u}zt =t~y{}

t~y{}



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~ {~

2rh 2r ( h + r) r2

h

2h (R + r) 2 ( R + r)(R r +h) h (R + r)(R- r)

rl r ( l + r) r2

h

tz ----------------- ------------------------- h( R2+ r

2+Rr)

4r2 ---------------------------

r3

------- --------------------------- ( R

3- r

3)

t 2r2 3r

2 r

3

t

2( R2+ r

2) (3 R

2+ r

2) ( R

3- r

3)

t{} tu} : : } 104

t{} ( tnpsc)

= 3 tu} = + + = 104

=104

= 96

t{} = = = 48

{} t 4 y t~y t

{} ~ ~ ~} u

{} t{}

t x} ~ x2

t ( x + 4) ~ ( x + 4) ( x + 4)

~ = ~

( x + 4) ( x + 4) = x2

( x + 4) ( x + 4) = x2

( x + 4) = x

2x + 8 = 3x

x = 8 {} t{}

y {} } ( tnpsc ){} tx y xy =



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{} t

{} = 4 t =

{} 10 % t~ } ~

t~z ( tnpsc ){} 100 y ~ 100y

{} 110 b ~ 110b

100 y = 110b

b=

b=9

9 % t~z

1 3

= 1000 y

1 3

= 1 y

1000 = 1 .

1000 .3

= 1

{} 50 % t~y t ~ t t

(tnpsc )

100 50 % ~ 150

4r2 = 4 100 100 =40000

4r2

= 4 150 150 =90000

~ = 50000 ~ = = 125

5 . 3 . {}

{} = 2 ( + ) = 2 ( 5 + 3 ) = 2(8) = 16 . {} t 20 .

{} = 4 x t = 4 x 20 = 80 .

{} 8 . 5 . ~{} ~ = x = 8 x 5 = 40 ..

{} t 7 . ~

~ = t x t = 7 x 7 = 49 ..

u t{} ~t 9 . 12 . ~

?

~ = x ~t x = x9 x 12 = 54 ..



12/51



1 .. x 1 .. = 1 rJu ..1 br.. x 1 br.. = 1 rJu br..1 . x 1 . = 1 rJu .1 .. x 1 .. = 1 rJu ..

1 } = 100 2

{} = a 3

{} u} zt 6

y {} 12 . } 9 . . y

{} = 12 9 = 3

9 . t {} = 4 t = 4 x 9 = 36

~t 12 . 5 . t{} ~

~ = bh = 12 5 = 30 ..

{} ~ 360 .2 } 15 .

~t

{} ~ = ~t

360 = ~t 15

~t = = 24 .

{} yu 9 . , 12 . ~

{} ~ = d1 d2

= 9 12= 54 ..

{} , , 8 . , 5 . , 2

. {} =

= 8 5 2 = 80 .

12,500 2 100 2 = 1

12,500 2 = 125

2.5 t yt

1 t = 10000 .

2.5 t = 2.5 10000 = 25000 .

10 , 3 , 27 . } ~ 25

. 12 . 9 . u {

} =

= 1000 300 27 100 . = 1



13/51



u} = 25 12 9

u =}

u}=1000 300 27

25 12 9= 3000

1 . , 10 t ~ 1 . t

20 } ~ = = 1000 10 = 10000 .

1 . t = 20

10000 . t = 10,000 20 = 2,00,000

} , , 5 , 3.4 , 4.5 .

} 4 t t . t 6

z

} = 2 ( + )

= 2 ( 5 + 3.4 )

= 2 8.4

= 16.8

} ~ = }

= 16 .8 4.5 = 75.6 .

75.6 . t t 75 . 6 6 = 453 .60

z y } . } } y 28

. } 7 y z

} = r2 h = 14 14 7 = 4312 .

4312 y

t{} y 56 . . 100 }

t{} y{} = 28

= 2 r= 2 28 = 2 22 4 = 176 .

100 = 100 176 = 17600 cm = 176 m

t{} tu3a + 4b - 2 , a 7 , 2a 4b + 3 }

}

= (3a + 4b 2 ) + (a 7) + (2a 4b + 3 )= 3a + 4b 2 + a 7 + 2a 4b + 3

= 6a 6

{} tu 3x + 2 , 5x + 4 } z

{} = 2 ( + )

= 2 (3x + 2 + 5x + 4 )

= 6x + 4 +10x + 8

= 16x + 12



14/51



y t . ~t 26

28 . y{v } yt 5 {

z .

y{} ~ = ~t

= 26 28 = 364

1 yt 5

182 yt = 364 5 = 1820

y~ 64 ~ { y{ ~{

-.

y } y 28 . }

yt 3 ~ = r 2= 14 14 = 616

616 yt 616 3 = 1848

y } 7

y~ . - y } ~ }

y{} ~ = r 2= 7 7 = 154 .

y 88 t z . ~tzt

y{} 2 r= 88

2 r= 88

r = =14

y{} ~ r 2= 14 14 = 44 14 = 616

{} = 4t = 88

t = 22

{} ~ = t t = 22 22 = 484y{} ~

t 2200 tt 100 .

t{} ~ z

100 = 2200

= 22

2 r= 22



15/51



2 r= 22

r=

t{} ~ = y{} ~ r 2= = 38. 5

28 . {} y .

t~y ~ . {} y{}

{} ~ z

y{} 2 r= 2 28 = 2 22 4 = 176 .

{} y{}

4 t = 176

{} t = 44 .

{} ~ = t t = 44 44 = 1936 ..

} , , 10 , 8 , 3 }

}}~z

} = 2 ( + ) = 2 ( 10 + 8 ) = 2 (18) = 36

}}~ = } = 36 3 = 108.

88 . y t~ . y{}

}

y{} = }

y{} 2 r= 88

2 r= 88

r= = 14 .

21 ,t{t~y{}

~z

~y{}y = {}t = 21 .

y{}~ = r 2= = 346. 5

21 . t { y | ~ y

y t~y y} ~ z

{} ~ = t t = 21 21 = 441 .

z t} y{} ~ = 346.5

y} ~ = 441 346 . 5 = 94 . 5 ..



16/51



11 . , 60 . , 61 . t u z

t{} ~ , za = 11

b = 60

c = 61

s = = = = 66

~ ==

=

=

= 6 5 11 = 330 cm = tu} = 11 + 60 + 61 = 132 .

{ ~y } ~ z

( {} t 28 . )

{}~ = t t = 28 28 = 784 ..

{} 4 14 .yu

4 y{}~=y{}~ = r 2= = 616 ..

~y = {} ~ 4 y{} ~

= 784 616 = 168 .2

u t{} ut{ t t

50 . 40 . . {} 25 . 20

. ~ ~ {} ~ = = 25 20 = 500..

u t{} ~ = bh = 50 40 = 1000 ..

u t{} ~

y } 35 .

t~y {} t }

y{} = 2r = 2 35 = 2 22 5 = 220

{} = 4 t = 220

t = = 55y ~ y{} {}

ABCD } ~

{} ~ = d ( h1 + h2)

= 10 ( 8+ 5) = 5 13 = 65



17/51



{} tu 20 % t~y } ~ {

t t

44 %

l}

b}~ lb

20 % ~ = l +

= b +

~ = ( l + ) ( b + )

= lb + + +

= lb + +

= ( 100 lb + 40 lb + 4 lb ) / 100

= 144 lb / 100

~ = - lb

= = = ~ =44 %

y{} , {} ~}

y{} = {} 2 r = 4 a

=

=

~}

= ( )

2= ( )

2=

=

t u t{} 6 + 3 } ~

t u t{} tu x , x}

~ x2 + x2 = 2

2x2 =2

= x

= x + x + x = 6 + 3

x

x



18/51



2x + x = 6 + 3

x (2 + ) = 3 ( 2 + )x = 3

~t = 3 .

= 3 .~~ = bh = 33= 4.5 m2

y u} 14 . yt 8

t

576 657 756 765

756

y{} = r + 2r= (+2 ) r

=( +2 )14 =( ) 14 = 14 = 36 2 = 72

1 yt 8

72 yt 72 8 = 576

ty{ 30 20 . y{

1.5 {yt 6

t~}{

o ) 495 ) 754) 854 ) 954

954

v{} = 30 + 1.5 + 1.5 = 33

v{} = 20 + 1.5 + 1.5 = 23

vt{}~ = = 33 23 = 759

t{}~ = = 30 20 = 600

}~ = v{}~ -

{}~

= 759600 = 159 .

1 yt = 6

159 yt = 159 6 = 954

}{} 5 : 7 }

4400 ..}

5x 7x }

=

4400 = 5x 7x

4400 = 22 5x x

4400 = 550 x3

x3

= = 8



19/51



x= 2

5x = 5 (2) = 10 .

u 7x = 7(2) = 14 .

{} ~ 33.32 .2 } t 8

. 5.6 . t ~ = h ( a + b )

33.32 = 5.6 ( 8 + b)

66.64 = 5.6 ( 8 + b )

66.64 =44. 8 + 5.6 b

66.64 44. 8 = 5.6 b

5.6 b = 21.84

b = = 3.9

42

.

yy{yy{yy{yy{

||||240

0

tttt

zzzz

yt~yt~yt~yt~yyyy{{{{}}}}uuuu}{}{}{}{

tttttttt}}}}~~~~

yt~}yt~}yt~}yt~}~~~~= = 42 42 = 3696 cm2

}}}}~~~~ = yt~}yt~}yt~}yt~}~~~~ = 3696

21212121 .... t t t t } {} ~y }} {} ~y }} {} ~y }} {} ~y }

~~~~

} } } }

{} ~{} ~{} ~{} ~ ==== tttt tttt ==== 21212121 21212121 ==== 441441441441 ........

} ~} ~} ~} ~ ==== {} ~{} ~{} ~{} ~ tt z y tt z y tt z y tt z y

~~~~ tt z y tt z y tt z y tt z y~~~~

{} ~{} ~{} ~{} ~ tt yy{} ~ tt yy{} ~ tt yy{} ~ tt yy{} ~

==== 441441441441 (((( ) =) =) =) = 441441441441 346346346346 ....5555 ==== 94949494.... 5555

} ~} ~} ~} ~ ==== 94949494 .... 5555

} ~} ~} ~} ~ ==== 94949494....5555 ++++94949494....5555 ==== 189189189189

~y } ~~y } ~~y } ~~y } ~ ==== {} ~{} ~{} ~{} ~ } ~} ~} ~} ~

==== 441441441441 189189189189 ==== 252252252252 ........

yy{} { { yy{} { { yy{} { { yy{} { { 37373737 ....

y{y{y{y{} ~} ~} ~} ~



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y{} y{} y{} y{} ==== 37373737

2 - r = 37r (2 - 1 ) = 37

r ( 2 - 1 )= 37

r ( ) = 37

r ( ) = 37

r = 7

~~~~==== 2222 ==== 7777 7777 ==== 154154154154

{} t {} t {} t {} t 4444 .... ~{ ~{ ~{ ~{ } ~} ~} ~} ~ 60606060

........ t ~ t{} ~{ t ~ t{} ~{ t ~ t{} ~{ t ~ t{} ~{

}}}}

6666....2222 .... 12121212 .... 5555....5555 .... 15151515 ....

tttt ~~~~

6666....2222 6666....2222 6666....2222 ==== 38383838....44444444

12121212 12121212 12121212 ==== 144144144144

5555....5555 5555....5555 5555....5555==== 30303030....25252525

15151515 15151515 15151515 ==== 225225225225

tttt ~~~~

10101010....2222 10101010....2222 10101010....2222 ==== 104104104104....04040404

16161616 16161616 16161616 ==== 256256256256

9999....5555 9999....5555 9999....5555 ==== 90909090....2525252519191919 19191919 19191919 ==== 361361361361

t t t t 5555....5555 t t t t 4444 t ~t ~t ~t ~ 60606060

tttt....

{} {} {} {} ,,,, 40404040 .... ,,,, 26262626 .... ....

v{} tu}v{} tu}v{} tu}v{} tu} ~ ~~ ~~ ~~ ~

{} ~ {} ~ {} ~ {} ~

| {} ~| {} ~| {} ~| {} ~ ==== {} ~{} ~{} ~{} ~

==== 40404040 26262626 ==== 520520520520 ........

C 20 .

~ = ~t x

300 = 15 x

= 300 / 15 = 20



21/51



C 40 .

~ = ~t x 800 = ~t x 20

~t = 800 / 20 = 40

D 600 .2

~ = ~t x

~ = 20 x 30 = 600

C

D 900

B 60 .2

( B ) h( a+b)

( A ) tu

h ( a+b) = x 15x 18 = 15 x 9 = 135

( D )

x h x 20 = 80h= (2 x 80 ) /20 = 2 x 4 = 8

( D)



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B

C z

A y

B 1 = 100 . = 100 / 2 = 50 .

D = 2 x

x 14 = 2x 22x 2 = 88 .

C

B ( ) r

A

y{} ~ = r2

= x 7 x 7 = 154

y{} ~ 154 /2 = 77

D 144 / 4 = 36

A

= 42

2 x x 42 = 2 x 22x 6 =44 x 6 = 264



23/51



y} =( y{} ) / 4 + 2r = 264 /4 + 84 =66 +84 = 150

D4

} B

180 C

90 A

C 84 x 2 = 168

.xU tl Mu Uklfhdh, gugs vjid klF mfF.A 2 B 3 C 4 D 1~ = r2

r = 2r

~ = (2r)2 = 4 r2 = 4 u

. xU rJu tot fhF nt mikf xU lUF %.4/- j%.1600/-brythwJ v fh gugs_______________

A 10000 10000 10000 10000 2222

B 1000 2

C 100000 2

D 400 2

1 yt 4

= y 4 y = 1600

y = 400

{} = 4t = y =400 t 100

~ = t x t = 100 x 100 = 10000 2

bfhLfgl rJu gugs 100 2. v Hlgl gFgu



24/51



A 15.5 2

B 12.5 12.5 12.5 12.5 2222

C 10.5 2

D 13.5 2

{ 8

~y 1

~y = 100 / 8 = 12.5

. xU miu tl Rws 36 br.. mj l (br-)A 7 B 35 C 22 D 14y{} = r + 2r = 36

r ( + 2 ) =36

r ( 22 / 7 +2) = 36r (22/7 + 14 / 7) =36r (36/7) =36

r = 7y = 2 x 7 = 14

xU miw s 30 kW mfy 20 v j miwia ug20 r.. gugs bfhl vjid jsuf njitgL?A 20 B 10 C 50 D 30~ = x = 30 x 20 = 600 .

~ = 600 / 20 = 30

y u} ~

~ z

{ , ~ t



25/51



z t tu | ~

u tu | ~

t tu | ~ u

y t 360 0

y{}t 180 0

y t 90 0

{}~utNa{}~t



26/51



3333 .... ,,,, 4444 .... ,,,, 5555 .... t } u t } u t } u t } u

t~y ~y } {t~y ~y } {t~y ~y } {t~y ~y } {

~~t z~~t z~~t z~~t z....

3333 .... t t t t {} {} {} {} ==== a3====3333 3333 3333 ==== 27272727 ....

4444 .... t {} t {} t {} t {} ==== a3====4444 4444 4444 ==== 64646464 ....

5555 .... t {} t {} t {} t {} ====a3====5555 5555 5555 ==== 125125125125 ....

t~y ~ t~y ~ t~y ~ t~y ~....

{} {} {} {} ==== 27272727 ++++ 64646464 ++++ 125125125125 ==== 216216216216 ........

a3 ==== 216216216216 ....

a==== 6666 ....

{ ~~{ ~~{ ~~{ ~~ ==== 6a2 ==== 6 6 6 = 216 cm2.

15151515.... t t t t t t t t 3333 .... t t t t

u { u { u { u {

15151515 .... t {} t {} t {} t {} ==== a3==== 15151515 15151515 15151515

3333 .... t {} t {} t {} t {} ==== a3==== 3333 3333 3333



27/51



u u u u ==== (15151515 15151515 15151515) (3333 3333 3333 ) = 125125125125

40404040 ....t | y t{t | y t{t | y t{t | y t{

y} ~ zy} ~ zy} ~ zy} ~ z .... } z } z } z } z| y} ~| y} ~| y} ~| y} ~ ==== 5a

2

= 5 40 40 = 8000 .. ====a3 = 40 40 40 = 64000 cm3

2 tttt}}}}zzzz. 10 .

tttt}}}}zzzz 50

z}z}z}z}{{{{}}}}

2 = 200 . tttt}}}}= a3 =200 200 200

10 . tttt}}}}= a3 =10 10 10

}}}}ztztztzt= (200 200 200 ) ( 10 10 10 ) = 8000

8000 }}}}zzzz= 8000 50 = 4 ,00 ,000

2124 zzzz}}}}}}}}7

}}}}y~y}y~y}y~y}y~y}

----yyyy~~~~, }}}}~~~~zzzz

----yyyy~~~~= 7

yyyy

4 ----yyyy~~~~= 7

y{}y{}y{}y{}~~~~

= 7 7 = 154 m2

= {}{}{}{}~~~~||||~~~~= ( 24 21 ) 154 = 504 154 = 350.

2 . }}}}uuuu}}}}}}}}

t~yt~yt~yt~y}}}}~~~~zzzz

~y~y~y~y }}}}~~~~= ttttttttABC }}}}~~~~3

y~}y~}y~}y~}~~~~

= a2

- 3 ( )

= 2

2

- 3 ( )= -

= 1.732 1.572 = 0.16

y

t y y y .

24 m

21 m

7 m

A

B

C



28/51



y =

p

n (z)

r y

= + y

365 y = 1 z

219 y = = z

73 y = = z

12 u = 1 z

6 u = = z

3 u = = z

y y

y- } { y y

y } .

yyA = P ( 1 + ) n

yy =

ztyyA = P 1 2n

ztyyA = P 1 4n

Pty r% zztyyt

yt{P ( )2

~{y

~{y{y =

~ y{ A =p n + I

p

n (u)

r y

A } =t {t

A ny ~ A }



29/51



~

t , t} v , {} ~ ,

y { z ~

} t A = P ( 1 + )n} {{~ }{

z

~

|u} ~ , z} ~ , y} ,

yu} ~ z }

t A = P ( 1 ) n} {{~ }{ z

} ~ a : b } b:a }

a:b } { ~ z} u

t u t

5 : 7 } {} | u

5 : 7

}

z t ( 2,3,4,5,6 ) }u

t

2 t

3 t

4 t

5 t

6 t

5 : 7 } u 10 : 14 , 15 : 21 , 20 : 28 , 25 : 35 , 30 : 42

u} t u

a:b :: c:d a x d = b x c( z} t=z} t )

12 : 9 , 4 : 3 } z t y



30/51



z} t{ 12 x 3 = 36

z} t{ 9 x 4 =36

z

12 : 9 , 4 : 3 } z

3 : 4 = 12 : y zt z

z} t{ =

z} t{

3 x y z = 4 x 12

3 x y z = 48

y z = = 16

z ~ { |

4 y 2 y . 2

y t y

y y

4 2

2 x

2 : 4 = 2 :x2x = 8 ~} zt = ~} ztx= 4

4 y

5000 t 5 % z y { 2 zt y

y = = = 50 x 2 x 5 = 500

t -

8 6 y ~ .

12 y { y y y

8 6

12 x8 : 12 =x : 6

12x = 8 6

x= 48 / 12 = 4 y



31/51



| 50,000 t . 2 %

{

50000 2 % = ( 50000 x 2 ) / 100 = 500 x 2 = 1000

1200 { - z 1100 t ~y

} ? = 1200 1100 = 100

1200 t = 100

100 t = = 8.33 %

{ z 5 % y { 5000 6000

y = 6000 5000 = 1000

y =

1000 =

1000 =50 n 51000 = 250 n

n = 4

100 | 6 % y { 5

zt { 5 z y{

p = 100 n = 5 z = 5 12 = 60 u

y = = 915

y y 3 z 3 u { 9

u { z

x 3 z 3 x

{ 3 z 3 x 3 (3 x ) = 9x

6 z 9 u

~y zt- y t 40

y . 45 | t 25 y . } { y} zt

y yx 40

x+ 45 25

x:x+ 45 = 25 : 40



32/51



40x= 25 (x+ 45 )

40x- 25x = 122515x = 1225

x= 1225 / 15 = 75

75 y

A } B } { 10 % B }

A} {

B } 100 }

10 % = 10

A } = B } + 10 %

= 100 + 10 = 110

110 t 10

100 t = = = 9

B} A} { 9

1500 z t 90 . 2000

z t {

1500 z t 90

2000 z t = = = 20

150 y 12 y ~ . 120 y

{ y ~

y y

150 12| | t t

120 x

120 : 150 = 12 : x120 x = 150 12

x = ( 150 12 ) = 15 y

276 y{ 20 yt{

. | y 46 yt t z { y{ y z

y

276 20

x 46x : 276 = 20 : 46

46x = 276 20

x = = 120



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| y 46 yt t z 120

y t z

| y 46 yt t z (276 120 ) 156

y{ y z

{{ 70 tu . t{ 30

v~ . t{ 20

vy { tu t ?

{ 70 30 = 2100

t{ 20 { tu = = 105

~y t 5 zt y 600

t { 8 zt y

z y5 6008 x

5 : 8 = 600 :x

5 x = 600 8

x = =960

8 zty 960

~y 35 ~ 7 z

} }35 z 7 100 t ?

} = = 20 %

u 36 u 5 u y .

u} }

36 { 5

100 t ?

u} = = 13 . 89 %

50 z ~ 23 . } ut z

~

50 23 50 23 =27

100 23 2 = 46 27 2 = 54

( 50 2 = 100 ) 46 %

54 %



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{ 75 t 66 ~z 80 t 72

| { ~z

{ 75 t 66

5 t = 4.4 80 t 72

5 t = 4.5

~z .

} 12, 000 . t 1200

~ } z

~ = 12000 t 1200

100 t = 10 % 100 % 10 % = 90 %

} { 25 % t t .

25000 {

25000 25 % = = 250 25 =6250

25 y . 36 % .

| y} zt

25 36 % = = 9| y 9

{ t 32 000 . 40 % z , 25 %

t | . z |}

zt

z 32000 40 % = = 12800| ( 100 % 40 % 25 % ) = 35 %

| 32000 35 % = =11200

|} 45000 . } 15 %t~ }

100 % 15 % = 85 %

45000 85 % = = 38250

y { 27 ,50,000 t u 2,50,000

. | y 33 ,00 ,000 t

y z

u 27,50,000



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2,50,000

t 30,00,000

33,00,000

= 3,00,000

=t = = 10 %

t 10 ~ u 100 t u. 2 ~

u y . u 11 t

. t { y z

1 {} t = = 10

u = 10 2 = 8

8 u = 8 11 = 88

y = 100

88 = 12

y =y

t= = 12 %

t 100 t 250 t u 1 4 t

. }

100 t u 250

100 t = 100 4 = 400

= 400 250 = 150

=t

= = = 60 %

40 u{ 360 t u

1 11 } t 36 .

4. 50 t 1 / y z

40 u u = 360

36 u = 36 11 = 396

4 u = 4 4.50 = 18

{ = 396 + 18 = 414

= u = 414 360 = 54

=t

= = = = 15 %

5000 t 10 % y { 5 z ~

y- - z

y

I = = = 2500

= + y = 5000 + 2500 = 7500



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1200 t 12 % y 3 z ~

y- - z

12 =

y I = = = = 6 3 25 =450

= + y = 1200 + 450 = 1650

z 10 % y u 10,000 ~

{ . 2 z 3 ut~

y z.

P = 10000

n = 2 z 3 u = 27u

r = 10 %y I = = = = 2250

2500 13 % zy ~v{ 146 y

z

y ~y 365 t z

t = 2500 , y = 13 % z

y I = = = = = 130

= + y = 2500 + 130 = 2630

12000 t 9 % z y 21 1999 | 2

1999 t y- - z

21 1999 | 31 = 11 y ( 31 20 )

} = 30 y

= 31 y

y = 1

{ = 73 y

y I = = = = = 216

= + y = 12000 + 216 = 12216

{ 6000 u { 5 z 7500

y z

= 6000

= 5 z

y = 7500 6000 = 1500



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y I =

1500 =

= = 5 %

10 % y { 2 zt 250 y{

tz

y = 250

=2 = z

y = 10 %

y I =

250 =

= = = 1000

{z 8 % y { 5000 5800

y = 58005000 = 800

y = 8 %

= 5000

= ?

y I =

800 =

= = 2 z

10 zy~y , z

100 }

t 200

y = 200100 = 100

= 10 z

y I =

100 =

= = 10 %

12 % z y {~yz

y~ . z}ztz



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= 100 }

t 200 ( y~ )

y = 200100 = 100

y = 12 % = %

y I =

100 =

= = 8z

~y 3 z 6500

1 z 5750 . y z.

+ 3 zy = 6500...................................(1)

+ 1

z

y= 5750...................................(2)

(1) , (2) tt 1 zy = 750

(2)

+ 750 = 5750

= 5750 -750 = 5000

3 z 6500

5000

y 65005000 = 1500

3 z

y ?

y I =

1500 =

= = 10 %

z 2 : 7 } { t .

z} 100 }}

zy :

2: 7 = 100 :x

2x= 100 7

x = = 350

----- : 1.5 = 6 : 4.5 y ?

6 1.5 = 4.5 x

x = = 2



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| 30 u 750 tu vt 4500

tuvt

t 750 30

4500 x750 : 4500 = 30 :x

750 x = 30 4500

x = = 180

750 t 30 ut

4500 t = = 180

3 : 4 tv

) 12 : 9 ) 6 : 10 ) 4:3 ) 6:8 6: 8

3 2 = 6

4 2 = 8

3:4=6:8

( z} t = z} t 4 6 = 3 8

150 3: 2 t t

) 50 90 100 120

90

3:2 3+2 = 5 u = 1501 u = 150 / 5 = 30

3 u = 3

tz

2:3 = 3:2 2:5 = 4:8 3:2 = 6:4 3:4 = 4:5

3:2 = 6: 4 3 4 = 12 , 2 6 = 12

10 t u~y 15 t ~y t

) 25 % 50 % 75 % 100% 50 %

= 15 10 = 5

10 t = 5

100 t = 50

50%

20 t u~y 10 t ~y



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) 25 % 50 % 75 % 100 %

50 %

= 20 10 = 10

=

t100 = 100 = 50 %

4 a = 3 b a : b = :

3 : 4 4 a = 3b | a / b= 3 / 4

2 : 3 3: 4

3,4 } .. 12

2 : 3 = = =

3 : 4 = =

Tnpsc Maths1

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