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Mixture and Alligation #4

4. Two vessels A and B contain spirit and water in the ratio 5 : 2 and 7 : 6 respectively. Find the ratio in which these mixtures be mixed to obtain a new mixture in vessel C containing spirit and water in the ratio 8 : 5 ?
A. 7 : 9B. 3: 4
C. 9 : 7D. 4 : 3

Answer: Option A

Explanation:

Let Cost Price(CP) of 1 litre spirit be Rs.1

Quantity of spirit in 1 litre mixture from vessel A $=\dfrac{5}{7}$
Cost Price(CP) of 1 litre mixture from vessel A = Rs. $=\dfrac{5}{7}$

Quantity of spirit in 1 litre mixture from vessel B $=\dfrac{7}{13}$
Cost Price(CP) of 1 litre mixture from vessel B = Rs. $=\dfrac{7}{13}$

Quantity of spirit to be obtained in 1 litre mixture from vessel C $=\dfrac{8}{13}$
Cost Price(CP) of 1 litre mixture from vessel C(Mean Price) = Rs. $=\dfrac{8}{13}$

By rule of alligation,

CP of 1 litre
mixture from
vessel A
CP of 1 litre
mixture from
vessel B
$\dfrac{5}{7}$$\dfrac{7}{13}$
Mean Price
$\dfrac{8}{13}$
$\dfrac{8}{13}-\dfrac{7}{13}=\dfrac{1}{13}$$\dfrac{5}{7}-\dfrac{8}{13}=\dfrac{9}{91}$

=> Mixture from Vessel A : Mixture from Vessel B
$=\dfrac{1}{13}:\dfrac{9}{91}=7:9$

Comments(6)

profileManish Kumar
2016-08-12 16:31:53 
let amount is 7x and  13y in vessels A and B respectively.

so, (5x+7y)/(2x+6y)=8/5
x/y=13/9

So ratio of amount in A/B =7x/13y =(7/13)*(13/9)=7/9
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profileNitin
2016-03-11 06:34:55 
I fail to understand that as per rule, cheaper quantity should be in the left extreme and dearer should be in the right and d-m and m-c. 7/13 is lesser than 5/7 then how formula changed completely?
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profilejiju
2016-03-18 09:37:35 
It does not matter. You can change the order and do the calculations accordingly (as given in this answer). Both will give you same result. Try and see.

Please go through "rule of alligation" and its proof (given by Raj under comments) under important formulas
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profileSai Arun
2015-04-03 03:40:23 
how u resolved this by simply putting spirit  and water ratio in vessel B 7/13 when it is 2/6 i.e 1/3 simplify properly do not adjust explain me theoritical clarification if u can 
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profilesaraswathi
2014-08-27 14:02:33 
Quantity of spirit in 1 litre mixture from vessel B = 7/13 how. Sir tell me immediately plz 
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profileAni
2014-09-01 17:35:11 
Vessel B contain spirit and water in the ratio 7 : 6

Quantity of spirit in Vessel B  = Total Quantity * 7/(7+6) = Total Quantity * 7/13

in 1 litre mixture , it is 1 * 7/13 = 7/13

Is it clear?
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