Alligation and Mixture - Exp

8/18/2019 Alligation and Mixture - Exp

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Alligation and Mixture

1. In what ratio must rice at Rs 9.30 per Kg be mixed with rice at Rs 10.80 per Kg so

that the mixture be worth Rs 10 per Kg?

Solution:

C.P o 1 Kg C.P o 1 Kg

rice o 1st rice o !nd

"ind #930p$ "ind #1080p$

% &

'ean Price

#1000p$

& %

#1080 ( 1000$ ) #1000 * 930$ 80 +0

,hus- reuired ratio / 80 ) +0 / 8 : 7

!. In what ratio must water be mixed with mi" costing Rs.1! per itre to obtain a

mixture worth o Rs.8 per itre?

2 the rue o aigation)C.P. o 1 itre o water C.P. o 1 itre o mi"

Ratio o water to mi" / ) 8 / 1 ) !

3. ,he cost o ,2pe 1 rice is Rs. 14 per "g and ,2pe ! rice is Rs.!0 per "g. I both

,2pe 1 and ,2pe ! are mixed in the ratio o ! ) 3- then the price per "g o the mixed

5ariet2 o rice is

6et the price o the mixed 5ariet2 be Rs. x per "g. 2 the rue o aigation- we ha5e )

Cost o 1 "g o t2pe 1 rice Cost o 1 "g o t2pe ! rice


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#!0*x$*14$ / !&3 /7 0 * 3x / !x * 30

/7 4x / 90 /7 x / 18.so, price of the mixture is Rs. 18 per kg.

. ow man2 "iograms o sugar costing Rs. 9 per "g must be mixed with !+"g o

sugar costing Rs.+ per "g so that there ma2 be gain o 10: b2 seing the mixture at

Rs.9.! per "g?

Solution:

6et the rate o second uait2 be Rs x per Kg.C.P o 1Kg wheat o 1st 980p

Step 1 :

;.P o 1 "g o mixture / Rs. 9.!


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4. ,he mi" and water in two 5esses B and are in the ratio )3 and !)3

respecti5e2. In what ratio the iuids in both the 5esses be mixed to obtain a new

mixture in 5esse c consisting ha mi" and ha water?

Solution:

'i" in 1 itre mixture o B / &+ itre.

'i" in 1 itre mixture o / !&4 itre.'i" in 1 itre mixture o C / 1&! itre.

2 rue o aigation we ha5e reuired ratio )D

) D

&+ !&4

% &

#'ean ratio$

#1&!$

& %

#1&! ( !&4$ ) #&+ ( 1&!$

1&10 1&1

;o Reuired ratio / ) D / 1&10 ) 1&1 / 7:"

. B !0 itre mixture o mi" and water contains mi" and water in the ratio 3) !. 10

itres o the mixture is remo5ed and repaced with pure mi" and the operation is

repeated once more. Bt the end o the two remo5as and repacement- what is the

ratio o mi" and water in the resutant mixture?

Solution:

,he !0 itre mixture contains mi" and water in the ratio o 3 ) !. ,hereore- there

wi be 1! itres o mi" in the mixture and 8 itres o water in the mixture.

Step 1. Ehen 10 itres o the mixture is remo5ed- itres o mi" is remo5ed and

itres o water is remo5ed. ,hereore- there wi be itres o mi" and itres o

water et in the container. It is then repaced with pure mi" o 10 itres. Fow the

container wi ha5e 1 itres o mi" and itres o water.

Step 2. Ehen 10 itres o the new mixture is remo5ed- 8 itres o mi" and ! itres o

water is remo5ed. ,he container wi ha5e 8 itres o mi" and ! itres o water in it.

Fow 10 itres o pure mi" is added. ,hereore- the container wi ha5e 18 itres o

mi" and ! itres o water in it at the end o the second step.

,hereore- the ratio o mi" and water is 18 ) ! or # : 1.

Shortcut.

Ee are essentia2 repacing water in the mixture with pure mi".

6et EGo be the amount o water in the mixture origina2 / 8 itres.

6et EGr be the amount o water in the mixture ater the repacements ha5e ta"en


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pace.

,hen-

Er& Eo/#1HR&'$n

where R is the amount o the mixture repaced b2 mi" in each o the steps- ' is thetota 5oume o the mixture and n is the number o times the c2ce is repeated.

ence-

Er& Eo/#1&!$!/ 1&

,hereore- Er/Eo& /8&

/!itres

ence the mixture wi ha5e 18 itres o mi" and ! itres o water.

+. ow man2 "gs o asmati rice costing Rs.!&"g shoud a shop"eeper mix with !4

"gs o ordinar2 rice costing Rs.! per "g so that he ma"es a proJt o !4: on seingthe mixture at Rs.0&"g?

Solution:

Step 1:

Bs the trader ma"es !4: proJt b2 seing the mixture at Rs.0&"g- his cost per "g o

the mixture / Rs.3!&"g.

Step 2:

C.P o 1 "g o rice o 1st "ind / Rs. !

C.P o 1 "g o rice o !nd "ind / Rs. !

'ean price / Rs. 0

2 the rue o aigation- we ha5e)

C.P. o 1"g o C.P. o 1"g o

rice o 1st rice o !nd

"ind #Rs. !$ "ind #Rs. !$

% &

'ean Price

#Rs. 3!$

& %

0 * ! ) ! * 3!

#8$ #10$6et the amount o asmati rice being mixed be x "gs.

8)10/x)!4 A x/2$ kgs.

Alternati%el&)

6et the amount o asmati rice being mixed be x "gs.

Bs the trader ma"es !4: proJt b2 seing the mixture at Rs.0&"g- his cost per "g o

the mixture / Rs.3!&"g.


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i.e. #x!$>#!4!$/3!#x>!4$

A !x>00/3!x>800

A 10x/!00 A x/2$ kgs.

8. In what ratio must a person mix three "inds o tea costing Rs.0&"g- Rs.+4&"g andRs.100 &"g so that the resutant mixture when sod at Rs.9&"g 2ieds a proJt o

!0:?

Solution:

The resultant mixture is sold at a profit of 20% at Rs.96/kg

i.e. 1.2 (cost ! Rs.96 !" #ost ! ! Rs.$0 / kg.

et the three &arities 'e ) *) and # costing Rs.60) Rs.+, and Rs.100 respecti&el-.

The mean price falls 'eteen * and #.

ence the folloing method should 'e used to find the ratio in hich the- should 'e mixed.

Step 1. ind out the ratio of # using alligation rule

Step 2. ind out the ratio of * # using alligation rule

Step 3. #) the resultant ratio of &ariet- c can 'e found '- adding the &alue of # in step 1 and step 2 ! 1 3 1 ! 2.

oe&er) in #T if -ou tr- and sol&e the pro'lem using the a'o&e method) -ou ill end up spending more than 2) and ma- 'e 4

minutes on this pro'lem) hich is a criminal mismanagement of time.

The 'est a- to sol&e a pro'lem of this kind in #T is to go from the anser choices as shon 'elo

The resultant ratio * # 1 5 2.

1 kg of &ariet- at Rs.60 is mixed ith 5 kgs of &ariet- * at Rs.+, and 2 kgs of &ariet- # at Rs.100.

The total cost for the + kgs ! 60 3 (5 +, 3 (2 100 ! 60 3400 3 200 ! ,60.

#ost per kg of the mixture ! ,60/+ ! $0 kgs.

9. B merchant mixes three 5arieties o rice costing Rs.!0&"g- Rs.!&"g and Rs.30&"g

and ses the mixture at a proJt o !0: at Rs.30 & "g. ow man2 "gs o the second

5ariet2 wi be in the mixture i ! "gs o the third 5ariet2 is there in the mixture?

;ame as pre5ious)

10. B merchant has 1000 "g o sugar- part o which he ses at 8: proJt and the restat 18: proJt. e gains 1: on the whoe. ,he uantit2 sod at 18: proJt is)

'xplanation:

2 the rue o aigation- we ha5e)

ProJt on 1st part ProJt on !nd part

8: 'ean ProJt

1:

18:


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Ration o 1st and !nd parts / ) / ! ) 3

Luantit2 o !nd "ind /3

x 1000"g

/ 00 "g.4

11.

;uppose 30 iters o a soution with an un"nown percentage o acoho is mixed

with 4 iters o a 90: acoho soution. I the resuting mixture is a !: acoho

soution- what is the percentage o acoho in the Jrst soution?30#x&100$ > 4#90&100$ / 34#!&100$.

/4+:

1!. B mi" 5endor has ! cans o mi". ,he Jrst contains !4: water and the rest mi".

,he second contains 40: water. ow much mi" shoud he mix rom each o the

containers so as to get 1! itres o mi" such that the ratio o water to mi" is 3 ) 4?

'i" in 1 itre mix. in 1st can

/

3

itreM C.P. o 1 itre mix. in 1st can /

Re.

3

'i" in 1 itre mix. in !nd can

/

1!

itreM C.P. o 1 itre mix. in !nd can /

Re.

1!

'i" in 1 itre o Jna

mix. /

48

itreM 'ean price /

Re.

48

2 the rue o aigation- we ha5e )

C.P. o 1 itre mixture in 1st canC.P. o itre mixture in

!nd can

3

18

'ean Price

48

1

!

18

Ratio o two mixtures

/

18

)18

/ 1 ) 1

;o- Luantit2 o mixture ta"en rom each

can / 1!

x 1! / itres.

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Alligation and Mixture - Exp