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Mixture and Alligation

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A pack of 240 ml, mixture of wine and water contains in the ratio 5: 7. How much wine must be mixed in the pack, so that the ratio of wine and water in the pack becomes 5:4?

  1. A) 75 ml B) 100 ml C) 115 ml     D) 125 ml
30 Answers

solution please


Solve by average 

(5*22.22 + 7*20)/12 =20.9


Hello Sir , kindly share the solution to this problem -

Since, the Selling Price  is not increased, to keep the profit percentage same the cost price of total mixture needs to be brought back to the original level by mixing the impurity 

CP ___________New CP 
to bring back to the original level  
120 ___________ 100 , % change = (20/120 ) x 100 = 16.66% = 1/6

So, impurity mixed is 1/6th of 12kg = 2kg . 

Alternative Approach: 

Use alligation rule 

[120]               [0]
[100]               [20]

5 : 1 

Hence impurity mixed is 1/6 of 12 = 2kg. 


A mixture of milk and water contain 30%milk. What % of mixyure should be replaced with milk such tjat resultant mixture contain milk and water in the ratio 11:14.

Hello Nancy! 

Let the total volume of mixture be 100ml 

and the volume of the replaced mixture be 10x ml 

[(30- 3x )+ 10x]/(70- 7x) = 11/14   

on solving we get, x = 2 

Hence replaced volume : 2 x 10 = 20 ml,  which is 20% of the mixture. 

Alternative Approach: 
% of milk in original mixture : 30% 
pure milk contains 100% milk 
% of milk in Final mixture : 11/25 x 100 = 44% 

[ 30%]                    [100%]


[1- x]                               [ x]

56                                     14i.e 

(1- x )/x = ( 100- 44)/(44-30) 

x = 1/5 i.e 20% 


How can we assume volume of replaced mixture 10x?


two glasses A and B contain milk and water mixed in the ratio 5:3 and 2:3. The ratio in which the liquid of these two glasses should be combined to form a new mixture containing half milk and half water is :

ratio of milk to total - 5/8   and  2/5

let's mix them in k:1

so ((5/8) *k + (2/5)*1)/(K+1) = 1/2

(25k + 16)/40 = (1/2)(k+1)

k =4/5

hence they should be mixed in the 4:5 ratio



a family uses a mixture of a blend of 2 coffees costing Rs30 and Rs 60 respectively. If the family uses only the expensive variety, it will have to spend Rs 450 more. The annual consumption of coffee of the family is 20 Kgs. In what ratio are the two blends being used ?

cost difference per kg = 30 (ie 30Rs will be extra paid when family shifts from cheaper to expensive coffee)

total difference 450, hence total extra kgs = 450/30 = 15 kg (ie 15 kg of cheaper coffee is replaced by 15 kg of expensive coffee)

so in the current blend there is 15 kg of cheaper coffee and 5 kg of expensive coffee.

Hence the ratio is 3:1



ritik and batik share a piece of land. the ratio of the area of ritik's portion to the area of batik's portion is 3:2. they each grow ghiya and tori on their piece of land. the entire piece of land is covered by ghiya and tori in the ratio 7:3 (by area). on ritik's portion of land, the ratio of area under ghiya to area under tori is 4:1. what is the ratio of ghiya to tori on batik's portion?  

piece of land 

Ritik - 3 (Ghiya - (4/5)*3 = 2.4

Batik -2 (Ghiya -(k*2) = 2k

Total -5 (Ghiya - (7/10)*5) = 3.5


so 2.4+2k = 3.5

k = 1.1/2 = 11/20

hence ratio of Ghiya to Tori = 11:9


a parantha shop in murthal gets an order of paranthas and 5 litres of lassi. the shop only has 3 litres of lassi at present. it decided to add water and curd to get 5 litres of lassi, which has 30% of curd by volume. if the original quantity of lassi had 40% curd by volume, how much water, in litres, did the shop owner add?

original lassi - 3 liters (40% curd)--> 1.2 litres curd (1200 ml), 1.8 liters water

5 liters lassi (30% curd) --> 1.5 liters (curd) and 3.5 liters water

Hence added quantity is 0.3 liters curd and 1.7 liters water


Bebe Sehgal is a musician who consumes a mixture of a concentrated drink 'Glucozade'
and Flavoured water 'Flavele' before a live show. She drank a 540 ml solution consisting
of 5% Glucozade and 95% Flavele but she feels most energetic when she consumes Glucozade and Flavele in the ratio 1:9 What quantity of pure Glucozade must she
consume to feel her best for the show?
A 30 ml
B. 60 ml
C. 120 ml
D. 240 ml

1:9 ration is 10% concentration

so using 5% and 100% , we have to make 10%

5 100
90 : 5

540 : 30

hence 30 ml of 100% concentration is required

hello sir, 
kindly help me out to solve this question.


A chemist sells 3 variants of a medicine of concentrations 30%, 50% , 80%. The original cost of 100% medicine is Rs 80/unit. If he wants to make a mixture of these 3  variants and sell this mixture at Rs 60/unit , what cant be the respective ratios to enable him to earn a profit of 25%? (Assume that Cp of the medicine equals only the cost of medicine contained in it)


From a vessel full of pure petrol, 6 litres of petrol was drawn out and replaced by kerosene. Again 6 litres of mixture was drawn out from the vessel and replaced by kerosene. the ratio of petrol to kersene left in vessel was 25:24. Then volume of vessel was?

A. 14

B. 15

C. 18


(1-6/x)^2 = 25/49 (Ratio of petrol to total is 25/49)
from above x= 21


A container contains milk and water in the ratio 5:3. after boiling the mixture 1.2 liters of water evaporated and the concentration of milk became 75%. find the original volume of the milk in the container if no amount of milk evaporated.   

This post was modified 3 years ago by tanvi

Q1. a milkman had 60 litres  pure milk. he sold 6 litres pure milk to anand and mixed 6 litres water. he then sold 6 litres of the mixture to bhima and mixed 6 litres water. again he sold 6 litres mixture to sima and added more 6 litres water. now he sold 6 litre of the mixture to rita and mixed  the same amount of water. 

find the difference between quantity of pure milk received by sima and that by rita. 

Q2. If milk man sold the  mixed milk at the rate of the cost price, then find the profit percentage earned from sima. 


a drunk man has three full glasses of mixture of wine and water in the ratio 1:4, 3:5, 1:3 in equal volume. he mixed all three mixtures into a bottle. what part of one glass should he mix pure wine into the bottle so that the percentage of wine in the bottle becomes 40%? 


singham, anand sanjay and mahindra have mixtures of two varieties of rice basmati and pusa in ratio 3:5, 5:7, 2:1, and 3:1 respectively. grocer x bought one quintal from singham and two quintal from anand and mixed it. grocer y bought three quintal from sanjay and 4 quintals from mahindra and mixed it. in what ratio binita should buy rice from grocer x and grocer y such that the ratio of basmati and pusa becomes 5:3? 

This post was modified 3 years ago by tanvi
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