alle2.pdf

8/9/2019 Alle2.pdf

1/12

Visit www.downloadmela.com for more papers

Download More Aptitude Questions,Reasoning questions,Puzzles

ALLIGATION OR MIXTURES

Important Facts and Formula:

1.Allegation:It is the rule that enables us to find the

ratio in which two of moreingredients at the given price must be

mixed to produce a mixture of a desired price.

2.Mean rice:The cost price of a unit quantity of the mixtureis called the mean price.

3.Rule o! Allegation:If two ingredients are mixed then

uantity of !heaper " uantity of #earer $

%!.& of #earer '() *ean &rice+ "%*ean &rice'()!.& of !heaper+.

C.P of a unit quantity of cheaper(c) C.P of unit quantity of dearer(d)

Mean Price(m)

(d-m) (m-c)

!heaper quantity:#earer quantity $ %d,m+:%m,c+

-.uppose a container contains x units of liquid from which y units

are ta/en out and replaced by water. 0fter n operations the

quantity of pure liquid $ x %1 '() y"x+n units.

SOL"E# RO$LEMS

Simple pro%lems:

1.In what ratio must rice at s .3 per 4g be mixed with riceat s 1.5 per 4g so that the mixture be worth s 1 per 4g6

olution:C.P of 1 Kg rice of 1st kind 93 p C.P of 1 Kg rice of !n d kind 1"p

Mean Price 1p

" #

http://downloadmela.com/pages/aptitude/aptitude-puzzles-logicalreasoning.htmlhttp://downloadmela.com/pages/aptitude/aptitude-puzzles-logicalreasoning.html

8/9/2019 Alle2.pdf

2/12



equired ratio$5:7 $ 5:7

2.8ow much water must be added to 9 liters of mil/ at 11"2 liters

for s 2 so as to have a mixture worth s 1 2"3 a liter6

olution:!.& of 1 lit of mil/ $ 22"3 $ -"3

C.P of 1 $it of %ater C.P of 1 $it of mi$k &'3

Mean Price 3!'3

"'3 3!'3

atio of water and mil/ $5"3 : 32"3 $ 1:-

uantity of water to be added to 9 lit of mil/ $1"-9$1; liters.

3.In what ratio must water to be mixed with mil/ to gain

2< by selling the mixture at cost price6

olution:=et the !.& of mil/ be e 1 per liter

Then .& of 1 liter of mixture $ e.1>ain obtained $2

8/9/2019 Alle2.pdf

3/12



;. -4g s of rice at s ; per 4g is mixed with 5 4g of rice

at s 9 per 4g .?ind the average price of the mixture6

olution:

rice of *s per Kg rice of *s per Kg

+,erage price +%

-+% +%-

%9,0w+"%0w,;+ $ -"5 $1"2

12,20w $ 0w,;

30w $ 170w $ ;.99 per 4g.

9.;4g of rice at s 9 per 4g is mixed with - 4g of rice to

get a mixture costing s 7 per 4g. ?ind the price

of the costlier rice6

olution:@sing the cross method:

rice at *s per Kg rice at *s per Kg

Mean price *s # per Kg

&

x,7:1$;:-

-x,25 $ ;-x$33$Ax$s 5.2;.

Therefore price of costlier rice is s 5.2; per 4g

SOL"E# RO$LEMS

Medium ro%lems:


8/9/2019 Alle2.pdf

4/12



1.0 butler stole wine from a butt of sherry which contained

-< of spirit and he replacedBwhat he had stolen by wine

containing only 19< spirit. The butt was then of 2-<

strength only. 8ow much of the butt did he steal6

olution:

ine containing &/spirit ine containing 1/ spirit

ine containing !&/ spirit

" 1

They must be mixed in the ratio of $1:2.

Thus 1"3 of the butt of sherry was left and hence the butler drew out 2"3 of the butt.

2.The average wee/ly salary per head of the entire staff

of a factory consisting of supervisors and the laborers

is s 9.The average salary per head of the supervisors

is s - and that of the laborers is s ;9.>iven thatthe number of supervisors is 12.?ind the number of

laborers in the factory.olution:+,erage sa$ary of $a0orer *s +,erage sa$ary of super,isors *s &

+,erage sa$ary of entire staff *s

3& &

Cumber of laborer " Cumber of upervisors $ 3- " -$5;"1

ThusBif the number of supervisors is 1Bnumber of laborers $5;.

Therefore if the number of supervisors is 12 number of laborers5;12$12.

3.The cost of type 1 rice is s 1; per 4g and type 2 rice

is s 2 per 4g. If both type1 and type 2 are mixed in the

ratio of 2:3Bthen the price per 4g of the mixed variety

of rice is6

olution:=et the price of the mixed variety be s x per 4g.

Cost of 1 Kg of type 1 rice *s 1 Cost of 1 Kg of type ! rice *s !


8/9/2019 Alle2.pdf

5/12



Mean Price *s

!- -1

%2,x+ "% x,1;+ $ 2"3$A 9,3x $ 2x,3

;x $ $Ax$15.

-.In what ratio must a grocer mix two varieties of tea worths 9 a 4g and s 9; a 4g so that by selling the mixture

at s 95.2 a 4g he may gain 1

8/9/2019 Alle2.pdf

6/12



Profit on 1st part "/ Profit on !nd part 1"/

Mean Profit 1&/

&

atio of 1st and 2nd parts $-:9 $2:3.

uantity of 2nd ind $3";14g $9 4g.

9.0 Dar full of whis/ey contains -< alcohol. 0 part of

this whis/ey is replaced by another containing 1< alcoholand now the percentage of alcohol was found to be 29

8/9/2019 Alle2.pdf

7/12



so their average price $s %129E13;+"2 $ 13.;.

o the mixture is formed by mixing two varieties Bone at

s 13.; per 4g and the other at say s x per 4g in theratio 2:2 i eB1:1 we have to find x.

Costof 1Kg tea of 1st kind * 13. Costof 1Kg tea of !n d kind *s .

Mean Price *s 13

-13 !!.

%x$1;3+"22.; $ 1 $Ax,1;3 $ 22.;x $ 17;.;.

&rice of the third variety $s 17;.; per 4g.

2.The mil/ and water in two vessels 0 and F are in the ratio

-:3

and 2:3 respectively. In what ratio the liquids in both thevessels be mixed to obtain a new mixture in vessel c

consisting half mil/ and half water6

olution:=et the !.& of mil/ be e 1 per liter.

*il/ in 1 liter mixture of 0 $ -"7 liter.

*il/ in 1 liter mixture of F $ 2"; liter.*il/ in 1 liter mixture of ! $ 1"2 liter.

!.& of 1 liter mixture in 0$e -"7

!.& of 1 liter mixture in F$e 2";.

*ean &rice $ e 1"2.

Fy rule of allegation we have:

C.P of 1 $iter miture in + C.P of 1 $iter miture in &'# !'

Mean Price 45

1'1 1'1&


8/9/2019 Alle2.pdf

8/12



equired ratio $ 1"1 : 1"1- $ 7:;.

3.8ow many 4g s of wheat costing him s 1.2Bs 1.--

and s 1.7- per 4g so that the mixture may be worth

s 1.-1 per 4g6

olution:tep1:*ix wheat of first and third /ind to get a mixture

worth s 1.-1 per 4g.

C.P of 1 Kg %heat of 1st kind 1!p C.P of 1 Kg %heat of 3rd kind 1#&p

Mean Price 1&1p

33 !1

They must be mixed in the ratio $33:21 $ 11:7

tep2:*ix wheats of 1st and 2n d /ind to obtain a mixtureworth of 1.-1.per 4g.

C.P of 1 Kg %heat of 1st kind 1!p C.P of 1 Kg %heat of !n d kind 1&&p

Mean Price 1&1p

3 !1

They must be mixed in the ratio $ 3:21$1:7.

ThusBuantity of 2n d /ind of wheat " uantity of

3rd /ind of wheat $ 7"111"7$ 11"1

uantities of wheat of 1st :2n d:3rd $ 11:77:7.

-.Two vessels 0 and F contain spirit and water mixed in


8/9/2019 Alle2.pdf

9/12



the ratio ;:2 and 7:9 respectively. ?ind the ratio n which

these mixture be mixed to obtain a new mixture in vessel

c containing spirit and water in the ratio 5:;6

olution:=et the !.& of spirit be e 1 per liter.

pirit in 1 liter mix of 0 $ ;"7 liter.

!.& of 1 liter mix in 0 $;"7.

pirit in 1 liter mix of F $ 7"13 liter.

!.& of 1 liter mix in F $7"13.

pirit in 1 liter mix of ! $ 5"13 liter.

!.& of 1 liter mix in ! $5"13.C.P of 1 $iter miture in + '# C.P of 1 $iter miture in #'13

Mean Price "'13

1'13 9'91

Therefore required ratio $ 1"13 : "1 $ 7:.

;.0 mil/ vendor has 2 cans of mil/ .The first contains ;<

water

and the rest mil/. The second contains ;< water. 8ow much

mil/

should he mix from each of the container so as to get 12 litersof mil/ such that the ratio of water to mil/ is 3:;6

olution:=et cost of 1 liter mil/ be e 1.

*il/ in 1 liter mixture in 1st can $ 3"- lit.

!.& of 1 liter mixture in 1st can $e 3"-

*il/ in 1 liter mixture in 2n d can $ 1"2 lit.

!.& of 1 liter mixture in 2n d can $e 1"2

*il/ in 1 liter final mixture $ ;"5 lit.

*ean &rice $ e ;"5.


8/9/2019 Alle2.pdf

10/12



C.P of 1 $t mi in 1st *e3'& C.P of 1 $t mi in !nd *e1'!

Mean Price '"

1'" 1'"

There ratio of two mixtures $1"5 :1"5 $ 1:1.

oBquantity of mixture ta/en from each can$1"212

$ 9 liters.

9.Gne quantity of wheat at s .3 p

er 4g are mixedwith another quality at a certain rate in the ratio 5:7.

If the mixture so formed be worth s 1 per 4g Bwhat is

the rate per 4g of the second quality of wheat6

olution:=et the rate of second quality be s x per 4g.

C.P of 1Kg %heat of 1st 9"p C.P of 1 Kg %heat of !nd 1 p

Mean Price 1p

1-1p # p

%1x,1+ " 7 $ 5"7

7x ,7 $ ;9

7x $ 7;9 $Ax $ s 1.5.

Therefore the rate of second quality is s1.5

7.5lit are drawn from a wine and is then filled with water.

This operation is performed three more times.The ratio of the quantity of wine now left in cas/ to that of the water

is 19:51. 8ow much wine did the cas/ hold originally6

olution:


8/9/2019 Alle2.pdf

11/12



=et the quantity of the wine in the cas/ originally be x liters.

Then quantity of wine left in cas/ after

- operations $ x%1, 5"x+-lit.

Therefore x%%1,%5"x++-+"x $ 19"51.%1, 5"x+-$%2"3+ -

%x, 5+"x$2"3

3x,2- $2x

x$2-.

5.0 can contains a mixture of two liquids 0 and F in theratio 7:; when liters of mixture are drawn off and the

can is filled with FBthe ratio of 0 and F becomes 7:.

8ow many liters of liquid 0 was contained by the caninitially6

olution:

uppose the can initially contains 7x and ;x liters

of mixtures 0 and F respectively .

uantity of 0 in mixture left $ %7x, %7"12+ +lit

$ 7x , %21"-+ liters.

uantity of F in mixture left $ ;x , ;"12

$ ;x , %1;"-+ liters

Therefore %7x '() 21"-+" %;x '() 1;"-E+$7"

%25x,21+"%2x E21+$ 7"%2;2x ,15+$ 1-x E1-7

112x $ 339

$A x$3.

o the can contains 21 liters of 0.

.0 vessel is filled with liquidB3 parts of which are water


8/9/2019 Alle2.pdf

12/12


and ; parts syrup. 8ow much of the mixture must be drawn

off

and replaced with water so that the mixture may be

half water and half syrup6

olution:

uppose the vessal initially contains 5 liters of liquid.

=et x liters of this liquid be replaced with water

then quantity of water in new mixture

$ 3,%3x"5+Ex liters.

uantity of syrup in new mixture $ ; , ;x"5 liters.Therefore 3 , 3x"5 Ex $ ; , ;x"5

;xE2- $ -,;x

1x $ 19.x$ 5";.

o part of the mixture replaced $ 5";1"5 $1";.

alle2.pdf

Documents