5 Percentage

8/2/2019 5 Percentage

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5 . P E R C E N T A G E l5.1 INTRODUCTIONThe word 'per cent' means per hundred. Thus. 19 per cent means. 19 parts out of 100 parts. TI; can alsobc wri 19c written as 100'

Therefore, per cent is a fraction whose denominator is 100, and the nu-nerator of this fraction is calledthe Rate percent. So, / ~ o = 19 per cent. Here, 19 per cent is the rate. The sign for per cent is '%'.

Table 5 .1 Fractional Equivalen ts of Im portan t Percen tages

~I ~ 4 16 241% = 2(/( = 8[;( = - 16'1( = 64'7, = 96'7, =10 0 50 25 25 25 ! 25 25-t----

'i'if I 10'Ir I 20'7rI 4-0 '7r 2 i 6 ( Y I < 3 80 'k 4 - 120[1r 6= = = = = =20 10 S S I 5 5 5

61 '7 r p (I l I I 2Y;( i 37 1 (C 3 s o r ( 87 I 0(7 IOWIr I= = = - , /( = = = =4 - 16 - ~ 8 4 - 8 2 1 8

I I 1 I I 1 1 I 5 1 4 -8 'I, 16 - (I r 33 C 66 - ' I e 83 r.: 13 3 c= = c = = ( = ( = -3 12 3 6 i . 3 3 3 3 3 6 3 3Note: Similarity along the horizontal rows are to be observed for memorizing table 5.1.

5.2 FRACTION TO RATE PER CENTTo convert (or express) any fraction f ; to rate per cent, multiply it by 100 and put a( o/c) sign.

ja1- x 100O/Cj b .

Ta fraction ~ rate per centExampll': Express 3 in rate per cent4Required rate per cent = 3 x 100O/C= 7S '7 (4


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5-2 Quantitative Aptitude for Competitive [vamilldtions5.3 RATE PER CENT TO FRACTIONTo convert a rate per cent to a fraction. divide it h: 100 and delete the ?c sign.f' I Ui b d to a f :-;"amp r-: "Ie can e converte - to a traction a, -.-1005.4 RATE PER CENT OF A NUMBERRate per cent of a number is the product of equivalent fraction (of rate ref cent' an j the number.

( p \~ po/, of A = ! ~ I x A\ 100 /Exampl! ' : To find out 250/, of 500SO/lIlio//. Required value = 250( of 500

= ( 25 J' x 500.\100~ equivalent fraction for 2,'i0/,

1255.4.1 Relation Among Rate Per cent, Number and ValueLet us consider a number, N.Then N is considered as the base over which value of different rate per cents are found out.

100/,- of N= 10 xN= N (value)100 10250/, of N= 25 xN= N (value)100 4

and so on.Therefore. it is found that as the rate per cent changes. its related value for the same number will also

change.Conversely. different values stand for different rate per cents of the same number. As in the above

example, N stands for 10cIc of N : N stands for 2,'ic0 of N and so (In.10 4In the above context, a very useful relation is derived as:

any value ')= number (base) Iits rate % of number ___) (1)E"ampl! ' : 9% of what number is 36')SO/lIlio//. Using the relation 1,

36the required number (base number) = 9 ' 7 c


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Percentage 5-3

36 x 1009= -1-00

Here. 36 is the value and its rate 'I r of base number = 9'7cIf 307< of a number is 48. then what is 70% of the number?Here. unitary method can be used to save the time.

300/ , ~ 48I'lc ~ 4830

7 0 9c ~ 48 x 70 = 11230nce. the required value is 112If 4 0 O / C of the number exceeds the 257< of it by 54. Find the number.

Using the formula ( l :any value-------- = number (i.e. base number)its rate r i C of number

54 stands for the difference of (409'( and 259'( of number)__ 5_4__ = number(40 - 25 )7

600 + 10 = 600x 3 x46~0 (~_ I ) = 10 => x = 20

(+ 10, for quantity availableincreases after rate change)


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Percelltage 5-9

Therefore. reduced rate = 2 x = 3 x 20 = Rs IS/kg.4 45.12 % EXCESS OR % SHORTNESS

When a number A exceeds the another number B by .r '7,. then '1 r shortness of B = 100 +1.r x 100

It implies that B is less than A by 100 + .1.r X 100"(.

.1Similarly. if a number A is short of (or less than) B b, . I r e . then r ; - excess of B = --- < 10 0100 - .1i.e. B is more than A by 100 - .r x IOO'iExampl t ' : If the income of Ram is more than that of Shyarn by .2Y;. then b;. I1m\ much pcrccntuje Shyamsincome is less than that of Ram';

Solution. Required '7 c shortness (less) income of Shyam x 100')(100 + 25= . 2W; .

Therefore. income of Shyarn is .20t; i lev than that of Ram.Solved Example.

E-! Express the following in terms of percentage:( a ) 0.4 (b) 1.0 ( e ) 5 (d) 7.1 ( e ) 1.233 I'

S-I ( a ) Refer 5.2, multiply the decimal fraction by 100... 0..+ = W.-t x 1(0) '7 c = 40 o/c,

(b) 1. 0 = (1,0 x 1(0) 0 / ( = 100 gc .

~ = p x I ( ) { ) ). ,

( e ) , ; = 166 = - C(,_, \ 3 3(d) 7.\ l 7 _ _ . ! _ _ x 100 J ti c = 700 x 0'c,=v Y , Y(e) 1.23 = (1.23 x 1(0) 'Ie = 123 0(,

E-2 Express the following in terms of fractions:( a ) " (i~ (b) 3)',; (/ (J,Y; ( e ) 7 f X( e ) c: (d).2 b .2


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5-10 Quantitative Aptitude for Competitive bamlnation


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Percentage 5-11

(e) 36 x 14 is what S of l -WO.(t) R is what 9 c of N.

5-4 Refer 5.5, the required percentage = ~ x 100 ''c, where .' is the base.i'

(a) Here. the base is 1-14. So , the denominator will be 14-1." d 36.. req"uire percentage = 144 x 100Q( = 25' 7( .

(b) Here, the base is 347 /8.. required percentage = x 100 9 c = 1163 /4

(c) Here, the base is 80.16., required percentage = x 100S = 20'7c.80

(d) Here, the base is 1 2.2 80.6251 728

x 10 0 = 50'1( .. required percentage =

(e) Here, the base is 140036 x 14 x 10 0 = 36 'K.. required percentage = 1-100

(t) Here, the base is N:. required percentage = R x 100 = l00R,;e.N N

E-5 Find the fo l lowing:(a) 36 is 6 c; ( of what"(b) 2.5 is 5 C jc o f what')(e) 12 is 25 i]( of 20 C jc o f what')(d) . is 24 C it o f what?7

5-5 Refer 5.4.1, using equation (1).anv value" " = Dumber (ori ainal lits rate '7c o f number ~

(a) required number = 36 = 36 x 100 = 600.69c 6(b) required number = 2.55% 2.5 100 0x = 5 .5

,j


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5-12 Q uantita tive A ptitude ior C om petitive E xam inations

(c) required number = 259c x 209c12 12 x 100 x 100 = 24025 x 20

(d) required number = 24 l 7c417 4 =_4_x 100=507 x 249c 7 x 24 21

E -6 25 % of a number is 20, what is 40 9c of that number? Also find the number.S-6 25 % -720=> 40 % -7 20 x 40 = 3225

any value 20Refer 5.4.1, using equation (1), the number = its rate 1(( 25%

=> required number = 20 x 100 = 8025E -7 P: % of number N] is equal to P2 % of number Nc . Find what per cent of N] is N2'lS-7 It is required to find what per cent of Nt is N2 , i.e. the base is N]

N 2required percentage = x 100%.N]p ] P2It is given that x N ] = X N2100 100

N2Putting the value of N] we find the required percentage = ( ! 2 . x 100I%Pc )N2 is equal to (;; x 100)%of N]

E -8 A number A exceeds B by 25%. By what per cent is B short of A ?S -8 Refer 5.12

% excess9c Short = - - - - - -(1 0 0+ 9c excess) x 100

= 25 x ]00 = 10(]OO + 25)E -9 A number X is short of Y by 40%. By what per cent is Y in excess of X?S-9 Refer 5.12. Using the formula,

% short% Excess = x 100100 - % short40 2--- x 100 = 66- %.

100-40 3


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Percentage 5-13

E-10 The ratio of salary of a worker in Julv to that in June was 2 _ ! _ : 2 _ ! _ . Bv what 0 / ( was the salary ofJ 2 4 .

July more than salary of June? Also find by what 9(. salary of June was less than of July.

Difference- --- Salary of June x 100

S-10 Let Salary of July 5 x2and 9Salary of June = - x4Refer 5.5, here the basis of comparison is either the salary of June or the saiary of July.Salary of July more than that of June by per cent

( ~ - : ) x9 x4

x 100= 11! o / e .9Salary of June less than that of July by per cent

( % - n x5 x2E-11 In 1987, the enrolment in a school was 1,500. Next year it increased by 10 o / c . What was the

= Difference x 100Salary of July = x 100 = 10%.

enrolment in 1988?S-l1 Enrolment in 1988 = 1500 x !~~1,650.E-12 The side of a square increases by p o / c , then find by what % does its area increase?S-12 Suppose, side of a square = b

Original area of the square = b2, i.e. result = A x BHere, both sides are increased by p%,So, for finding out the % change in area, Refer formula (2A).

.rvNet % change in area = x + y + _._, where, x = \ ' = + P100 .,p-~ Net % change in area = p + p + -100

p C= 2p + 100

Hence area increases by ( 2 p + L ) %.100


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5-14 Quantita tive Ap titude for Competitive EXJm ina tio !ls

Note: This formula is also applicable when the radius of a circle is increased by p%.I ',I " P Y !Then its area increases by i 2p + '\.-. ! S'c.L 10/ JE-13 The daily wage is increased by 15 0(. and ;1 person now gets Rs 23 per day. What was his daily wage

before the increase'?Increased daily wageS-13 Original daily wage = x 100100 + c k increase [R efer 5 .8 /. . . , ~~ x 100 = 20115

NB: -7 / 1 / case of dec r ease use (- ) Ie sign. before 'i c value.E-14 "p' litres of oil was poured into a tank and it was still e 0( empty. How much oil must be poured into

the tank in order to fill it to the brim. Find the capacity of the tank.S-14 Suppose. 'x ' litres are to be poured to fill the tank completely, then, x = e S'( of capacityNow, P + e S'c of capacity = full capacity e . .=> P + 100 x capacity = capacity

p x 100=> capacity = lOO-e eS'ce P x 100" x = eo/c of capacity = x .---- litres100 lOO-e P litre

pex = litres = amount of oil to be poured to fill the tank completely.100-('E-IS A student X passes his examination with 51 5 marks. having scored 30( above the minimum. If Y had

obtained 710 marks. what 9( would he have been above the minimum?

SOlS Marks of YMarks of X100 + 7 c above minimum of Y100 + 0 / ( above minimum of X

710 100+ Y => Y = + 42 qS IS 100+3Hence Y gets 42% above minimum.Note: Similarly, if the % marks is below minimum. formula would have been.Marks of Y 100 - % below mini mum of YMarks of XRemember.Marks of YMarks of X

100 - % below minimum of X

100 % above/below minimum of Y100 % above/below minimum of X

Here, (+) ve sign indicates above minimum and (-)ve sign indicates below minimum.


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Percentage 515E-16 If a J~ X m ore then /J and b i, \ci- less than a. find the rela tion be tween x and Y.S-16 !Re/i'l 512/

v------- x I O O ~ (100 - .\\" ~< 100 100+ \

100 x.\Y _-- = >100 +.\

=> v X 100NB: \. and X u:,p,e.lt'llt onl: the numerual value. i .. it a IS 3c-( 11101(' than /J put 011/" x = - ' .

E-17 The ra tio o f num ber o f boys and g lrb in a schoo l is 3 2 if 200', o f the boy , and 2S'} 01 the g irlsare ho lding : scho larship . find the '( o f schoo l studen ts who(a) h ol d s ch ol ars hip(b) do no t ho ld scho la rship

S-17 Percentage of scho la rship ho lde rs= (Boys x (I ( hoy , who are scho la rship ho lders) + (Girls x t ic g irls who are scho la rship holders)

(~ \ (, \- [ __:- x ,() I. + I ---- x ''iI - "_ . ' i I - _ . 1 - ........\2+~ ) 1 \ 3 4 - 2Sim ila rly . pe rcen tage o f non scho la rship ho lders =(Since IO ()- 20 = RO . 100 - 25 = 75 )E-18 Groundnut oil is now be ing so ld at Rs 27 per kg . During la s t m on th its COSI was Rs 2-+ per kg. Findh} how much c( a family should reduce It s consumpt ion . ,(1 as to keep the expenditu re the sam e .

S-IS New ra te = Rs 27 /kgO rig in ~li ra te = = R s 2-1 ./ kg .

Change in ra te = 27 - 2-+ = Rs :;Here . the r;( change in consum p tion can be found ou t directly withou t finding the 0( change in ra teby the fo llow ing sho rt-ou t m ethod.

Short-rut: ra te ch an geSince. C( change in ra te =o ld ra te

l()()

So, - ra te change (observe the diffe rence in the( f chan ge in co nsum ptio n = x 100New rate denom ina tor o f these two fo rm ula)

-:I x I DO % = = -I 1 L c : ,27 9Hence . faru j 1:- h as to reduce its con sum p tion by 11 1%.9

I.~,. .j$


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E-19 A reduction of Rs ~ pet : ' ) C enables a man to purchase - + kg m ore suga r to r Rs 16. F ind the orig ina lprin' of sugar .

S-19 I kiL' expenditure if i' i xed (= Rs 161. hu t as the ra te reduces (b) Rs ~/kg I, so. th e q ua ntity of suga ravailable increases Ih ) - + kg l. L e t o rig ina l p rice be R, x/kg . thing the fo rm u la 3 [R ctcr 5 .1 1 !

\1'L'n.iltU(l ' ~ l'h ~lllg L ' in quamit. ,(\ .ulablc = F\[1cllciiture:\l'\\ rail'

: : : : : > c ~ \ - : - ; = Il : : : : : > 1\ = - + 1 1\ - ~ I = (I : : : : : > . \ ' = - + (, r -2Consilkrin g till' +vc value, ()rig(ll~li pncl' = Rs ~ pe r kg.

1':-20 If the price o f cotfcc is increased hy Y c. hy ]1


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Percentage 5-17S-23 We know that. expenditure = price x consumption.

So. new expenditure becomes II ()(y of 30110 '0 132 .- x _, = x ne\\ consumpnon100 100New consumption = 2skg.

IExpenditure increases by 1Olff JE-24 A man's income is increased bv Rs l. 2()() and at the sam e tim e. the rate of tax to be rid is reduced

from IYIr to 10q. He now pays the same amount of tax as before. What is his increa ed income if209', of his income is exempted from tax in both cases?

S-24 Since. the same percentage of his income i- , exempted from tax in both C'hes. this data is not to beconsidered.Now. let . v be the increased income.Amount of Tax! = Amount of Tax;(x - 12(0) x 12'7c = .r x 109',..r = Rs 7,200 = income after increase.

E-2s When N is reduced by - J . . it becom es 80', o f itself. What is the value of V'(Bank P.O. '91)

S-2s The problem implies that 1100 - 80) r;~ of . v = .+209'( of N = .+ I V = .+ x 10020 (Since 100 - 80 = 20)

N= 20.E-26 When N is increased by 6. it becomes I02c; of itself. What is the value of N'!S-26 The problem implies that

(102 - 100) 9', of N= 6

(IA '84)

Ylc of N = 6 ~ N = 6 x 100. . ,N = 300.

E-27 Increase(i) 200 h) 60 C ;( liil II b-, I()() I(

(iii) 35 by 200 9'( (i v) .+ 8 b) 12 (I,2(v) 1000 by 3.5 q

100 + PS-27 If a number (IV) is to be increased b) p ' 7 r then multiply N by 100 [Refer 5.81(i ) So. 200 becomes 200 x 1100 + 60)100 I.e. 320.

100 + 100( i i ) II increases to II x 100IOO+p(iii) Increased number = N x I O ( )

i.c, 22.

= 35 x IO O + 200100 105.


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5-1 B Q ua ntttative A ptitu de 'IH CO!~7petl';\ e C"';')lfldti(


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.---.--.-.------~----.-----

621")= 216 x 100I")-= 216 _:'Ix 2 C X )

= 216 5 135.- =8100 - P(iv) Decreased number = N x --- lO a

= 300 x 100 - 2.5100= 3 x 97.5 = 292.5.

100 - P(v) Decreased number = N x 100

= 1000 x10015100

= 10 x 499 = 998.5

100 - p(vi) Decreased number = 1 1 / x ---100100-121

")= 50 x 100 ,17 5= 50 x 200

= 50 x 7 = 43.75.8E-29 If 10% of an electricity bill is deducted. Rs 45 is still to he paid Hem J l 1 1 1 , ' h \\~h th e bill)S-29 Here Rs 45 refers to (l00 - 10) q- of thc hill.

Since 900/, of bill = 451 0 0 O / C of bill = 45 x 100 = 5090

Hence the bill was 50.The weight of a sand bag is 40 kg. In a hun-yo it was weighed as 40.8 kg. Find the error percentage.(Bank PO '89)


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5-20 Quantitative Aptitude for Competitive Exam inationsFalse weight - Actual weightS-30 o / c Error = x 100Actual weight40.8 - 40

40The error is 2 o / c .

x ]00 = 2'7c

E-31 If the price of one kg of cornflakes is increased by 25 '7c . the increase is Rs 10. 7ind the new priceof cornflakes per kg. (c.n.s '86)

S-31 Using the formula (I)Difference in priceOriginal price = x 100Difference in per cent

10 x 100 = 4025.. New price = 40 x 125 = 50100. . New price of cornflakes per kg is Rs 50.

E-32 The price of a book is reduced by 25%, what is the ratio of(i) change in price to the old price?(ii) old price to the new price?

Also find(iii) the factor by which the old price should be multipl ied to give the new price.

S-32 Consider the old price = Rs 100.Change in price 25 1(i) = -=-Old price 100 4Old price 100 4(ii) = =New price 75 3

(iii) Refer 5.8100 - pDecreased price (new price) = old price x . where p = 25100

New price = old price x ( ] J _ )1003So the required factor is 4

E-33 If A is more than B by 10%. then find(i) B = A x ?(ii) A = B x ?(iii) A =?B


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Percentage 5-21Since A is more than B by 10%,

100 + 10100(i) So A = B x

~ B = A x 1011(ii) A = B x !!.. 10

A =B100 + 10100

A 11.. B 10If X is 20% less than y, then find(i) .!_ = ?Y

Y-X(ii) = ?yX

Y-X = ?Since X is 20% less than Y, therefore(i) XY

XY

100 - 20100

45

(ii) X is 20% less than Y , therefore, if Y is 100 then X is 80Y-X 100 - 80~ =------Y 100Y-X 1.. --=Y 5X 80--=Y-X 100 - 80X 4--=Y-X 1

If 2 _ !_ % of the weight of a table is 0.2 kg, then what will be 120% of it") (C.D.S '83)2I2 - % of weight = 0.2 kg (use the unitary method)2


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5-22 Quant/tat!1 e ""pI/lucie f u r C ( )!~ ll )t :u t :\ e hammell/oil'

= > 12() ' ; 0 .2 x 12 0 = 1) 2 X 120~I x 2 = 9.6

1 2W ( o f the weighr o f the table i~ 9.6 kg .

R EGULA R PR O BLEM S i(]) The num ber O .O ':= ;hIIh at p erc C'n ta ge o f 2Cr:

(a) I . ' :=; (b ) DO:: ' :=; (C ) 0.25 Id l . , - (e ) 25.)I :: IS 0.2'; o r'(u) ::..+00 (b) 600 Ic l : : . . .W (d ) 6000 (e ) 2

(2)

(3) ln a n e le ctio n . one o f the two candida tes got 30',( o f the to ta l votes polled . bu t he iost by 210 votes .W ha t was the to ta l num ber o f votes polled' . 'la l 525 Ihl 700 Ie ) 610 Id ) 300 (e) ' : = ; : : 0(4 ) There arc 850 studen ts in a class . Ou t o f these . ..j.-+':C are M uslim s. 281/ , Hindus. 10q Sikhs andrem ain ing studen ts be long to the o ther comm unities . How m any studen ts a re there of o ther comm u-nities') (RRB Secunderabad, '01)(a) 173 (b) 1..13 Ie) 15 3 Id ) 16 3 Ie ) 13 3

(5) The p rice of an article is cu t by 10':i. to resto re to its o rig in al v alu e. the new price m ust be increasedbvla ) IOq Ib ) 9 J . . . . q..II (e) 11 'I t II d) 11 '7 (9 (e) 909c

xHint: Use the concep t: if A is 1';( le ss than B. then B exceeds A by C i ' c100 - xnew price o rig in a l price

(6) T he diffe re nce between ( )n e . .fifth of 1000 and one-fifth per cen t of 1000 is :r .n SOU (hi SO IC) 19::) Illl4 liS Ie ) 017 ) A m an spend, < " l m ' i- of hi, in com e and saves the re -,r. W ha t percen tage o f his expenditu re does he

. S < I ve(a) ~() (b) 25 IC) - ' 0 ill) .+0 (e I Data insufficient

(8 ) ]5'~; of .v subtracred from .r i., equa l III m ultip lying .v by which num ber?Ia) ()]5 b 23I) -20 (c) 115

1720

0.85Ie ) 100(9) A pudding is m ade 'If ..j.OO gm sugar. 200 gm of eggs, 1)00 gm of flour and 100 gm of dry fru it. The

percentage of sugar p resen t in the pudding is :

(10)(a) 11~ 'X9I f I f/k of ' + O ( i f(a) 20()

I b) ..j.O'} 7(d) 26 - ~ 7 c3( d) 32 5

(e ) 12 J '7 (7o f a num ber is 8 then the num ber is

(b) 2::':= ; Ic) 125 (e) 512(11) The radiu s o f it circle is so increased tha t its circum ference increases by 5'1(. Then the area of the

circle w ill in cre ase by:la) 10';1r (h) ::5';( IC ) ]0.::5'1( (d) 12.5'1t (e) S C 7 cHint: Refer 5 ] ()


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-----_-__-------- ---------- Percentclge 5-23----_------_l 40';f o f th e popula t ion of a town are m en and 3'i1":( are w om en . It the num ber o f children are 20000.

then the num ber of m en will be:(;1) 3200 rb) 80000 (c) 32(J ()() Id) .~.21J .()OO. Ie) 2.1)0.000

) A m edical stude III ha s to secure -1 -0 '; m a rk s to pu--. He tC'\' :-)()and fu il-, 1:) \ N) m arks. F in e ! th em axim um m arks .(a) l'iO (b) 2'i0 'e I 3'iU lei 'i(I(JHint : Refer 5.-1.1. Here . m axim um m arks h th e 1bu-,e t n um ber, becau se c ; pas , m .rrks i,re i, -d as-10,) ;- o f m axim um m arks

~) 4U'k of th e s tu de nts of a co llege a re fro m \\'e ,t Benga l and ou t of this. -H)'.~(arc In \ 11 Kolk.irn. , 'hat'j( of the s tuden ts a re nu t from Kolk.ua?(a) 60 ih) 16 (C ) -10 r c I 21 )

')A school ha s a s tuden t population of 'i60. T he num ber of girh is I -J . -:;. c ;- of th e num ber of boy- Howmany girls are in the schoo l'.'(a) 100 t b) 70 Ic) :-)() t d I 141) lei 2-1-0.. JHint: 14 '-:' q7 7

) /\ man saves 3 + 'il from his su lary o t R s 7:'i() e\e r) mon th . In hov, many mom h- \\ iII he he able tosave an amount equa l to his monthly -ularv'(a) 40 m onths r b I : 'iO month -, ( c I .'0month , IL it -J.: ' imonths Ie I ' . . : u ll e I I I the-.c

1 I n an cxum ination .. P' 'cored 130 poin ts. which arc 10 poi Ilt, abo ve -.tIY ;'. an d (j scored 7'/(. Thep oin ts sco re d by Q a rc(a) 22:'i (b I 2'iUWhen 7 5 ( . i c o f a num ber i, added til(3) 15 0 Ib) 30 0

Ie' I 2 0 0 Id I 2 " 7 'i7". th e resul t i, the num ber again. The num ber islei I()I) lell 4:,1l Ie) ."50) T he percen tage 01 to tu l q ua ntity re prese nted by a 12 ' sector ill a circle g raph ,p ie diag ram ) i-,

(a) 1 2 0 l - Id I ,I c;b) 24 '(Hint : Total quanti ty in ;1 circle g ra rh t p ic d id gra ;n I " 31M]J the p rice o f SLtg.:lr i- , in creased b:, 71;. then b:- Ilu\\ much PCI' Cent shou ld a hcu scv ife reduce herconsumption of -ugur. Hi hci\L' til! c\lra expenditure1;.,1 7 over ]07' , Ihl 107 over I OW (i;!) ],;, Ie; ~ > 3 U\lT I ( JO ' > ;

Ie) IO() on'!' 107'(

Hint : Rele I' 'i.](). I\Vhat is the l


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5-2 4 Quantitative Aptitude for Competnr;e Examinat ion,(24) Nagamani had a car to sell. Loknayak offered him a sum of money for the car that he refused as it

was 139(, below its value. Loknayak then offerrcd R, 450 more and the second offer was 51(( morethan the estimated value. What was the value of the car?(a ) R s 3000 (b) Rs 2500 (C I Rs 3800 (d) Rs 2800 (e) None

Answers1. (c) 2. (d) 3. (a) 4. (C I 5. (d) 6. (c) 7. (b) 8. (j) 9 . (d)

10. (c) 1 1 . (c) 1 2 . (c) 13. (C I 14. (d) 15. (b) 16. (e) 17. .) 18. (h)19. (d) 20. (a) 2 1 . (c) 22. (h) 23. (bl 24. (b)

REAL PROBLDIS(1) Which number is 409c less than 360')

(a) 90 (b) 144 (c) 216 (dl 270 (e) 2S8(2) p is 6 times that q. By what per cent is q less than p')

83 _ l_ ')(a) 500 (b) (c) 5 (d) 20 16 :3 - '(3) If 9(Ylc of A = 30ck of B and B= x9r of A . then the value of .v is

(a) 600 (b) 800 (c) 900 (d) 300 (e) None(4) If 1 . of 2 of 4 of a number is 12 then 30 per cent of the number will be8 3 5

(BSRB, Chennai, 2000)(a) 48 (h) 64 (c) 54 (d) 42 (el None of these

(5) A piece of cotton cloth 20 m long, shrinks by 0.5',( after washing. The length of the cloth afterwashing is(a) 19.5 m (b) 19.9 m (cj 19.95 m (d) 19.92 m (e) 19.05 m.

(6) The percentage by which 120 is to be diminished to get 90 is:(a) 30 (b) 25 (c) 20 (d) 33'!_

(RRB Kolkata, '01)(e) None of these

(7) Two numbers are 209c and 251(( less than the third number. By how much per cent is the secondnumber to be enhanced to make it equal to the first number?(a) 62 (b) 6 1 (c) 25 (d) 33 1343 ie) 20Tips: When any number 'x' is related to two or more than two numbers in terms of percentage, thenit is convenient to assume .r = 100

(8) 2 over 3 is? per cent of 5 over 7. The value of e n is(a) 90 (b) 93.33 (c) 94 (d) 9 (e) None of these

(9) There is an increase of 30lk in the production of milk chocolates in Amul Dairy in one month. If nowit is 9100 milk chocolates per month. what was it one month ago?(a) 13000 (b) 10300 (c) 8~00 (d) 7000 (e) 11700

(10) A positive number is by mistake divided by 6 instead o f heing multiplied by 6. What is the S l c erroron the basis of correct answer?(a) 3 (b) 97 ((;) J 7 (d) 83 (ei 100


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Percentage 5-25When 30 per cent of a number is added to another number the second number increases to its 140per cent. The second number = x C i r o f the first number. The value o f .r is

(Bank of Baroda PO, '99)(a) 130 I(C ) 133 3 1(d) 33 3 (e) 110b ) 7 5If the length of a rectangle is increased by 20% and the breadth is reduced by 20%, what will be theeffect on its area') (Guwahati PO. '9)(a) 40/, increase (b) 67 < increase (c) 4'1r decrease (d) No change (e) None' of the-eIf the height of a triangle is decreased by 407< and its base is increased by 4 O C I c . wnat will he lleeffect on its area') SBI PO, '(9)(a) No change (b) 16 ' Ic increase (C ) W;; - decrea se Id) 16"; decrease (e) None of the-eIf tw o numbers arc respectively 20 '1c and 50 '7c of the third number. then what q. is the first nun -e rof the second?(a) 30 (h) 70 (e) 40 (d ) .10 Ie) 50.In measuring the side of a square. an error o f 5 ( ; ; - in excess is made. The e rro r p erc en ta ge in rh ecalculated area is(a) 10 14

~(b) 10.::..4 ( c ) 5(C I 1 4A number exceeds by 40 when added by 20r;; of itself. The number is(a) 200 (b) 60 (C I 80 (dl 32 0 Ie) 12 0A rainy day occurs once in every 25 days. Half of the rainy days produce rainbows. The percentageof days having no rainbows is(a) 2 (el 50d) 87 I

")(c) 98

In a class of 52 students. 259r are rich and others are poor. There are 20 females in the class. of whom55ck are poor. How many rich males are there in the class" ("IABARD, '96)(a ) 13 (b) 4 (c : 39 Id) 2 (el 28When any number is divided by 12. then dividend becomes of the other number, By how much4per cent is first number greater than the second number? (BSRB, Chennai, 2000)(a) 200 (bl 150 (C) 30 0 (d) data inadequate (e) ","oneNaresh's monthly income is 300/( more than that of Raghu. Raghus monthly income IS 209c less thanthat of Vishal. If the difference between the monthly incomes of \' aresh and Vishal is Rs 800. whatis the monthly income of Raghu? (Baroda PO, '99)(a) Rs 16000 (b) Rs 20000 (C I Rs 12000 (d) Data inadequate Ie) NoneHint: Since the difference of income has been given in respect of Naresh and Vishal. So. at first. findthe relation of income for Naresh with Vishal and equate the difference.The rate for admission to an exhibition was Rs 5 and was later reduced by 20 ' 7c . As a result. the saleproceeds increased by 4 4 9 c .The percentage increase in attendance was:(a) 80 (b) 24 (cl 64 (d) 20 (el None of theseHint: Rate x attendance = sale proceeds


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5-26 Qua nt/te ltile A ptitu cle (or Compd/t i \ to ' hall7!llatiu{),(22) An ore contains -1-0'!(mass impurity. while the metal extracted from this ore contains 4% impurity.

How much metal will 2-1-tons of the ore yield'(a) 10 tons (b) 2() tons (e) 9 tons Id) 12 tom (e) 15 tonsTips: Since only pure part of the ore yields metal. So. equate the pure (quantity) part in the ore andpure pan in the metal.

(23) At an examination in which maximum marks are 500 . .-\ got lOr;; less than B, B got 25% more thanC. C got 20';( less than D. If A got 360 marks, what percentage of marks was obt. ned by IY'(a) 60 (b) 72 IC) 55 id) SO (e) H lHint : Since D is the last in the c - ; - relation. so assume the marks obtained by D = \ "

Answers1. (C J 2. (b) 3 . (d) 4. (e) 5 . Ib) 6. Ib) 7. lal 8. (l 9. (d)

10. (h) 11. rb i 12. IC) 13. (d ) 14. (e I 15 . (a) 16. (al 17 . (el 18. (b)19. (d) 20. (a) 21. (a) 22. Ie) 23. (dl

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