Mixtures & Alligations Tips & Tricks

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INTRODUCTION TO MIXTURE AND ALLIGATION:

Hi Aspirants today we are going to discuss on a topic Mixture and Alligation. This  topic carries 1 mark in prelims and 2 mark in mains exam.This topic can be implemented in Topics such as Time and Distance ,Ratio and Proportions.

MIXTURE:

When two or more components are mixed together then it is known as Mixture

Mixture is of two types they are:

1.Simple Mixture:When two or more different ingredients are mixed together,a simple mixture is formed

2.Compound Mixture:When two or more simple mixtures are mixed together, a compound mixture is formed.

ALLIGATION:

It enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture  of desired price.

Where M=Mean Value which is between X and Y, X=Cheaper Price, Y=Price higher than the Mean Value

#.1.TYPE 1:

MIXTURE CONTAINING TWO OR MORE INGREDIENTS:

1.A Shopkeeper Sells Rice Of 1kg For Rs.75 W Two Quality Of Rice Whose Worth For 1kg Is Rs.70 And Rs.80.

Therefore for 1kg of rice the two quality of rice should be mixed in the ratio  1:1

TYPE  2:

BASED ON PROFIT OR LOSS:

1.A Dishonest  Milkman Professes To Sell His  Milk At Cost Price But He Mixes It With Water And Thereby Gains 25%.The Percentage Of Water In The Mixture?

Let the Cost Price of  Pure Milk be Rs.1,

Selling Price of (Milk+ Water) is also Rs.1. which is 25% more than the Costprice

Therefore CostPrice = (100/125)*1=(4/5)

The Percentage   of water mixed in the mixture =*100=20%

2.The Ratio ,In Which Tea Costing Rs.192 Per Kg Is To Be Mixed  With Tea  Costing Rs.150 Per Kg So That The Mixed Tea  When  Sold For Rs.194.40 Per Kg,Gives A Profit Of 20%.

Quality	Cost Price	Selling Price	Selling Price after Profit/Loss
1st Quality	150		194.40  after 20% profit
2nd Quality	192

Finding   Selling Price after Giving Profit over Cost Price:

Let the Cost Price be X

Selling Price=X*(120/100)  = 194.40

X=(19440/120) ⇒ X=162

     

30:12   ⇒        5:2

The 1^st and 2^nd quality of rice should be mixed in the ratio:5:2

Remember:

If there is a loss in the transaction indicate it by the ‘-‘ negative sign before the number.

TYPE 1:

BASED  ON THREE INGREDIENTS OR THREE RATIO’S:

1.The Grocer sells apples of 3 varieties whose price per kg’s are Rs.40,Rs.60  and Rs. 90 .If he sells 1kg of apple by missing all these 3 varieties for Rs.80 what is the ratio by which these varieties are to be mixed?

2.Tea worth Rs.126   per kg and Rs.135 per kg are mixed with a third variety in the ratio 1:1:2.If the mixture is worth Rs.153 per kg, the price of the third variety per kg will be?

3.There are three vessels of equal capacity holds milk and water in the ratio of 1:2,2:3 and 1:4if the content of all the three vessel s are mixed in asingle vessel then.Find the ratio of milk and water in the new vessel?

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TYPE 2:

BASED ON REMOVING AND ADDING SOME QUANTITY :

1)How much water must be added to 60 litres of milk at 1.5 litre for Rs.20,So as to have a mixture worth Rs.10 2/3 per litre?

2)In a 729 litres mixture of milk and water ,the ratio  of milk to water is 7:2.To get a new mixture containing milk and water in the ratio 7:3,the amount of water to be added is?

3)8 litres are drawn from a cask filled with wine and is then filled with water .This operation is performed three more times.The ratio of the quantity of wine now left in the cask to that of the total solution is 16:81.How much wine does the cask originally ?

4)A vessel contains mixture of liquids A and B in the ratio 3:2.When 20 litres of the mixture  is taken out and replaced by 20litres of liquid B,the ratio changes to 1:4.How many litres of liquid A was there initially present in the vessel?

IMPORTANCE OF MIXTURE AND ALLIGATION:

Mixture and Alligation is used in other Miscellaneous Topic such as

Ratio and Proportion

Time and Distance

You can reduce the time taken to solve the problem if you use Mixture and Alligation Method

#.1.TYPE 1:

BASED ON ALLOYS:

1.A milk vendor has 2 cans of milk. The  first contains 25% water and he rest milk.The second container 50% water.How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3:5?

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2.The milk and water in two vessels A and B are in the ratio 4:3 and 2:3  respectively .In what  ratio  the liquids in both vessels be mixed to obtain a new mixture in vessel c consisting half milk and  half water?

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#.2 TYPE 2:

FINDING NUMBER  OF PERSONS :

1.In  a zoo there  are Rabbits and Pigeons.If heads are counted ,there are 200 and if legs are counted there are 580.How many pigeons are there?

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2.The total number of people in the village is 5000.If the male and female increases by 10% and 15% respectively,the population of the village becomes 5600.What is the number of male in the village?

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#.3. TYPE 3:

PARTIAL WORK:

1.A shopkeeper sells 1000kg of sugar ,part of which he sells at 8% profit and the rest at 18% profit .He gains 14% on the whole. The quantity sold at Rs.18% is?

1)A Jar Contains A Mixture Of Milk & Water In The Ratio 4:1.When 10 Litres Of The Mixture Is Taken Out & 10 Litres Of Water Is Poured Into The Jar,The Ratio Becomes 2:3.How Many Litres Of Milk Was In The Jar?

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PRACTICE THIS SUM:

1)A Vessel Contains mixture of liquids A and B in the ratio 3:2.When 20 litres of the mixture is taen out and replaced by 20 litres of liquid B,the ratio changes to 1:4.How many litres of liquid A was there initially present in the vessel?

2)A can contains a mixture of two liquids in proportion 7:5.When 9 litres of mixture are drawn off and the can is filled with B,the proportion of A and B becomes 7:9.How many litres of liquid A was contained by the can initially?

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#.2.TYPE 2:

BASED ON DIFFERENT CAPACITY:

1)Three glasses of Sizes 5 litres,10 litres & 15 litres contain mixture of Milk & Water in the ratio 3:2,4:6&4:11 respectively.The Contents of all the three glasses are poured into single vessel.Find the ratio of Milk to Water in the resultant mixture.

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PRACTICE THIS SUM:

1)Three bottle of Capacity 6 Litres,12 Litres and 4 litres contain mixture of Sugar water and honey in the ratio 1:5 , 7:5 & 1:3 respectively.The contents of all the three bottles are poured into single bottle.Find the ratio of Sugar water to honey in the resultant mixture?

2)Four glasses of sizes 2Litres,8 Litres,12 Litres & 16 Litres contain mixture of milk & Water in the ratio 1:1 ,3:5,7:5,9:7 respectively.The Contents of all the four glasses are poured into single glass.Find the ratio of Milk & Water in the resultant Mixture?

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#.3. TYPE 3:

 BASED ON RATIO’S:

1)In an Alloy,Zinc and Copper are in the ratio 3:4,In the Second alloy the same elements are mixed in the ratio 7:2.In what ratio should these two alloys be mixed to form a new alloy in which the two elements are in the ratio 5:6?

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PRACTICE THIS SUM:

1)In An Alloy The Zinc & Copper Are In The Ratio 1:3.In The Second Alloy The Same Elements Are In The Ratio 4:3.In What Ratio Should These Two Alloys Be Mixed To Form A New Alloy In Which The Two Elements Are In The Ratio 4:5?

2)A jar full of lime juice contains juice and sugar water in the ratio 2:3.In the 2nd Jar the same elements are in the ratio 7:2.In what ratio should these two elements be mixed to for a new alloy in which the two elements are in the ratio 6:5?

Practice Sets On Mixtures & Alligations

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• Vikram covered 180 km distance in 10 hours. The first part of his journey he covered by Car, then he hired a Rickshaw. The speed of the car and rickshaw is 25 kmph and 15 kmph respectively. The ratio of the distances covered by the car and the rickshaw is
  A. 7:9
  B. 7:3
  C. 7:5
  D. 7:2
  E. 7:4
  Answer & Explanation

  Answer – C. 7:5
  Explanation :
  Average Speed = 180/10 = 18kmph
  15………………….25
  …………18…………..
  7…………………….3
  The ratio of time taken by rickshaw to car = 7:3
  The ratio of distances covered by rickshaw to car = 7 * 15 : 3 * 25 = 7:5
• A mixture of wheat is sold at Rs.3 per Kg. This mixture is formed by mixing the Wheat of Rs.2.10 per kg and Rs.2.52 per kg. What is the ratio of price of cheaper to the costlier quality in the mixture if the profit of 25% is being earned
  A.2:5
  B.2:1
  C.2:3
  D.2:7
  E.2:9
  Answer & Explanation

  Answer – A.2:5
  Explanation :
  Selling Price = x + 25*x/100 = 3; x = 2.4
  210………………….252
  …………240…………..
  12…………………….30
  2:5
• From the 50 liters of a chemical solution, 5 liters of chemical solution is taken out and after it, 5 liters of water is added to the rest amount of chemical solution. Again 5 liters of chemical solution and water is drawn out and it was replaced by 5 liters of water. If this process is continued similarly for the third time, the amount of chemical solution left after the third replacement
  A. 32.75L
  B. 30.80L
  C. 36.45L
  D. 30.25L
  E. 38.50L
  Answer & Explanation

  Answer – C.36.45
  Explanation :
  50 * 45/50 * 45/50 *45/50 = 36.45L
• From a container of milk, which contains 200 liters of milk, the seller replaces each time with water when he sells 40 liters of milk(or mixture). Every time he sells out only 40 liters of milk(or mixture). After replacing the milk with water 4th time, the total amount of water in the mixture is
  A. 75.82L
  B. 81.92L
  C. 85.28L
  D. 87.45L
  E.None of these
  Answer & Explanation

  Answer – B. 81.92L
  Explanation :
  The amount of Milk left after 4 operations  = 200(1-40/100)⁴
  = 200 *(4/5)⁴= 200 * 256/625 = 81.92L; Amount of water = 200 – 81.92 = 118.08L
• A jar was full with Milk. A person used to draw out 20% of the Milk from the jar and replaced it with water. He has repeated the same process 4 times and thus there was only 512 gm of milk left in the jar, the rest part of the jar was filled with the water. The initial amount of milk in the jar was:
  A. 1.50 kg
  B. 1.30 kg
  C. 1.40 kg
  D. 1.25 kg
  E. 1.75 kg
  Answer & Explanation

  Answer – D. 1.25 kg
  Explanation :
  Shortcut:
  512 = x(1-1/5)⁴
  x = 1.25 kg
• From a container of Milk, a thief has stolen 15 liters of milk and replaced it with same quantity of water. He again repeated the same process. Thus in three attempts, the ratio of Milk and water became 343:169. The initial amount of Milk in the container was: 
  A.140 litre
  B.130 litre
  C.125 litre
  D.120 litre
  E.115 litre
  Answer & Explanation

  Answer – D.120 litre
  Explanation :
  Milk(Left) = 343
  Milk(Initial amount) = 512
  343x = 512x(1 – 15/y)³
  (1-15/y) = 7/8
  y = 120 litre
• The ratio of Solution “A” and Solution “B” in the container is 3:2 when 10 liters of the mixture is taken out and is replaced by the Solution “B”, the ratio become 2:3. The total quantity of the mixture in the container is:
  A.25L
  B.20L
  C.30L
  D.45L
  E.None of these
  Answer & Explanation

  Answer – C.30L
  Explanation :
  Initial = 3:2 ; After replacement = 2:3
  2/3 = (1 – 10/n)
  n = 30L
• From a container, 6 liters Solution “A” was drawn out and was replaced by water. Again 6 liters of the mixture was drawn out and was replaced by the water. Thus the quantity of Solution “A” and water in the container after these two operations is 9:16. The quantity of the mixture is:
  A.35L
  B.25L
  C.20L
  D.15L
  E.10L
  Answer & Explanation

  Answer – D.15L
  Quantity of solution “A” = x(1-6/x)²
  Solution “A” : Water = 9 : 16
  Solution “A” : Solution “A” + water = 9:25
  x(1-6/x)²/x = 9/25
  x = 15L
• The diluted Milk contains only 8 liters of Milk and the rest is water. A new mixture whose concentration is 30%, is to be formed by replacing Milk. How many liters of the mixture shall be replaced with pure Milk if there was initially 32 liters of water in the mixture?
  A. 3 litre
  B. 4 litre
  C. 8 litre
  D. 5 litre
  E. None of these
  Answer & Explanation

  Answer – D. 5 litre
  Explanation :
  Milk : Water
  8 : 32 => 1:4
  Original Ratio = 20%:80%
  Required Ratio = 30%:70%
  Original Ratio(water) = 80%
  Required Ratio(water) = 70%
  7/8 = (1-x/40)
  x = 5 litre
• In a school, the average weight of boys in a class is 30 kg and the average weight of girls in the same class is 20kg. If the average weight of the whole class is 23.25 kg, what could be the possible strength of boys and girls respectively in the same class?
  A. 18 and 19
  B. 13 and 27
  C. 16 and 15
  D. 15 and 13
  E.None of these
  Answer & Explanation

  Answer – B. 13 and 27
  Explanation :
  20…………………….30
  …………23.25…………..
  6.75…………………….3.25
  Total number of boys and Total number of girls = 13 and 27

 

• A vessel is filled with liquid, 4 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
  A.1/9
  B.1/10
  C.1/5
  D.1/12
  E.1/7
  Answer & Explanation

  Answer – B.1/10
  Explanation :
  Suppose the vessel initially contains 9litres of liquid.
  Let x litres of this liquid be replaced with water.
  (4-(4x/9) +x) = (5-(5x/9))
  X = 9/10
  So, part of the mixture replaced = 9/10 * 1/9 = 1/10
  Shortcut:
  4:5—->9
  1:1—->2
  8:10
  9:9
  1/10
• Rice worth Rs. 126 per kg and Rs. 134 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 177 per kg, the price of the third variety per kg will be:
  A.254
  B.216
  C.224
  D.238
  E.262
  Answer & Explanation

  Answer – C.224
  Explanation :
  126*1+134*1+2x=177*4
  260+2x=708
  2x==708-260=448
  x=448/2 = 224
• One quantity of rice priced at Rs 9.30 per Kg is mixed with another quality at a certain rate in the ratio 8:7. If the mixture so formed be worth Rs 10 per Kg, what is the rate per Kg of the second quality of wheat?
  A.12.75
  B.10.80
  C.15.50
  D.20.25
  E.18.50
  Answer & Explanation

  Answer – B.10.80
  Explanation :
  Let the rate of second quality be Rs x per Kg.
  9.30…..…………x
  …………10………….
  8………………………7
  7X – 70 = 5.6
  X = 10.80
• How many kgs of rice of variety-1 costing Rs.42/kg should a shopkeeper mix with 25 kgs of rice of variety-2 costing Rs.24 per kg so that he makes a profit of 25% on selling the mixture at Rs.40/kg?
  A.15
  B.20
  C.25
  D.30
  E.None of these
  Answer & Explanation

  Answer – B.20
  Explanation :
  25% profit by selling the mixture at Rs.40/kg, his cost per kg of the mixture = Rs.32/kg.
  (x×42)+(25×24)=32(x+25)
  42x+600=32x+800
  10x=200
  x=20kgs.
  Shortcut:
  125 = 40
  100 = 32
  42……………….24
  ………32…………..
  8…………………….10
  10 = 25
  8 = 20
• An alloy contains Brass, Iron and Zinc in the ratio 2:3:1 and another contains Iron, zinc and lead in the ratio 5:4:3.If equal weights of both alloys are melted together to form a third alloy, then what will be the weight of lead per kg in new alloy?
  A.5 1/9
  B.1/4
  C.4 1/7
  D.1/8
  E.2/7
  Answer & Explanation

  Answer – D.1/8
  Explanation :
  Shortcut:
  In the first alloy,
  2:3:1     =6*2
  5:4:3 =12
  Multiply 2 to make it equal,
  4:6:2
  5:4:3
  Adding all,
  4:11:6:3=24
  3/24=1/8
• A can contains 50 litres of milk. 10 litres of this milk is taken out and replaced with water. This process is repeated twice. Find the amount of remaining milk in the mixture? 
  A.127/3 litres
  B.26 2/3 litres
  C.87litres
  D.128/5litres
  E.27 2/3 litres
  Answer & Explanation

  Answer – D.128/5litres
  Explanation :
  Remaining milk = 50 [1 – (10/50)]³ = 128/5
• A milkman mixes 6 litres of free tap water with 20litres of pure milk. If the cost of pure milk is Rs.28 per litre the % Profit of the milkman when he sells all the mixture at the cost price is
  A.25%
  B.16.5%
  C.30%
  D.16(1/3)%
  E.None of these
  Answer & Explanation

  Answer – C. 30%
  Explanation :
  Profit=28*6=728
  Cp=28*20=560
  Profit = 168*100/560=30%
• Rs 4000 is lent in 2 parts, 1 part at 8% per annum and 2nd part at 12% per annum. At the end of a year Rs 400 is received as simple interest. Find the part lent at 8% p.a.
  A.3500
  B.2500
  C.2000
  D.1500
  E.1000
  Answer & Explanation

  Answer – C.2000
  Explanation :
  Effective interest rate = 400/4000*100 = 10
  8…………………12
  ……… 10………..
  2…………………..2
  1:1
  1/2*4000 = 2000
• A 144 litres of mixture contains milk and water in the ratio 5 : 7. How much milk need to be added to this mixture so that the new ratio is 23 : 21 respectively?
  A.36 litres
  B.40 litres
  C.28 litres
  D.32 litres
  E.30 litres
  Answer & Explanation

  Answer – D.32 litres
  Explanation :
  144 == 5:7
  60 : 84
  Now == 21 = 84
  23 = 92
  92-60 = 32
• In a 100 litre mixture of milk and water, the % of water is only 20%. The milkman gave 25 litres of this mixture to a customer and then added 25 litres of water to the remaining mixture. What is the % of milk in the final mixture?
  A.68%
  B.57%
  C.60%
  D.53%
  E.None of these
  Answer & Explanation

  Answer – C.60%
  Explanation :
  80: 20 == 4:1
  25 == 20:5
  60 : 15
  60 : 15+25 == 60:40
  60%

 

• Two vessels A and B contain a mixture of Milk and Water. In the first vessel (i.e) Vessel A has the ratio of Milk to water is 8 : 3 and in the second vessel, Vessel B has the ratio of 5 : 1. A 35 litre capacity vessel is filled from these two vessels so as to contain a mixture of Milk and water in ratio of 4 : 1. Then how many litres should be taken from the first vessel, Vessel “A”.
  A. 12 L
  B. 17 L
  C. 14 L
  D. 11 L
  E. None of the Above
  Answer & Explanation

  Answer – D. 11 L
  Explanation :
  [8/11(x) + 5/6(35-x)]/[3/11(x) + 1/6(35-x)] = 4/1
  x = 11
• When one litre of water is added to a mixture of milk and water, the new mixture contains 25% of milk. When one litre of milk is added to the new mixture, then the resulting mixture contains 40% milk. What is the percentage of milk in the original mixture?
  A. 100/6 %
  B. 50/6 %
  C. 100/3 %
  D. 50/3 %
  E. None of the Above
  Answer & Explanation

  Answer – C. 100/3 %
  Explanation :
  Original Mixture = x L
  In (x + 1) Mixture, quantity of milk = (x + 1)* (25/100) = (x + 1)/4
  one litre of milk is added to the new mixture
  [((x + 1)/4 )+ 1 ]/ x + 2 = 40%
  x = 3 ; quantity of milk = (3 + 1)/4 = 1L
  percentage of milk in the original mixture = 1/3 * 100 = 100/3 %
• The price of a box and a pen is Rs.60. The box was sold at a 40% profit and the pen at a loss of 10%. If the Shop keeper gains Rs.4 in the whole transaction, then how much is the cost price of Box?
  A. Rs.10
  B. Rs.30
  C. Rs.20
  D. Rs.40
  E. None of the Above
  Answer & Explanation

  Answer – C. Rs.20
  Explanation :
  40x/100 – 10(60-x)/100 = 4
  40x + 10x = 400 + 600
  x = 20
• A vessel contains a mixture of diesel and petrol in which there is 20% diesel. Five litres are drawn off and then the vessel is filled with petrol. If the diesel present in the mixture is now 15% then how much does the vessel hold?
  A. 10 L
  B. 20 L
  C. 30 L
  D. 40 L
  E. None of the Above
  Answer & Explanation

  Answer – B. 20 L
  Explanation :
  20/15 = x/x-5
  x = 20
• In a lab, two chemical solutions Acid “A” with 90% purity and Acid “B” with 96% purity are mixed resulting in 24 litres of mixture of 92% purity. How much is the quantity of the first solution, Acid “A” in the resulting mixture?
  A. 12 L
  B. 20 L
  C. 16 L
  D. 14 L
  E. None of the Above
  Answer & Explanation

  Answer – C. 16 L
  Explanation :
  90x + (24 – x)* 96 = 24 * 92
  x = 16
• 60 kg of a certain variety of Sugar at Rs.32 per kg is mixed with 48 kg of another variety of sugar and the mixture is sold at the average price of Rs.28 per kg. If there be no profit or no loss due to the new selling price, then what is the price of second variety of Sugar? 
  A. Rs.25
  B. Rs.23
  C. Rs.29
  D. Rs.27
  E. None of the Above
  Answer & Explanation

  Answer – B. Rs.23
  Explanation :
  Total CP of first variety = 60 * 32 = 1920
  Total CP of second variety = 48 * x = 48x
  SP of Mixture = 1920 + (108 * 28) = 3024
  1920 + 48x = 3024 => x = 23
• Six litre of milk was taken out from a vessel and is then filled with water. This operation is performed two more times. The ratio of the quantity of milk now left in vessel to that of the water is 8 : 27. How much is the quantity of the milk contained by the vessel originally?
  A. 18 litre
  B. 16 litre
  C. 14 litre
  D. 12 litre
  E. None of the Above
  Answer & Explanation

  Answer – A. 18 litre
  Explanation :
  [x(1-6/x)/x]³ = (8/27)
  [x(1-6/x)/x]³ = (2/3)³
  (x-6)/x = 2/3
  x = 18
• A vessel is filled with 120 litres of Chemical solution, Acid “A”. Some quantity of Acid “A” was taken out and replaced with 23 litres of Acid “B” in such a way that the resultant ratio of the quantity of Acid “A” to Acid “B” is 4:1. Again 23 litres of the mixture was taken out and replaced with 28 litre of Acid “B”. What is the ratio of the Acid “A” to Acid “B” in the resultant mixture?
  A. 43 : 29
  B. 46 : 23
  C. 47 : 21
  D. 46 : 29
  E. None of the Above
  Answer & Explanation

  Answer – D. 46 : 29
  Explanation :
  In 23 litre mixture, Quantity of Acid “B” = 23 * 1/5 = 4.6 litre
  Acid “A” in the mixture = 23 – 4.6 = 18.4 litre
  120 – x / 23 = 4 / 1
  x = 28
  Ratio = 92-18.4 : 18.4 + 28
  Ratio = 46 : 29
• 18 litres of Petrol was added to a vessel containing 80 litres of Kerosene. 49 litres of the resultant mixture was taken out and some more quantity of petrol and kerosene was added to the vessel in the ratio 2:1. If the respective ratio of kerosene and petrol in the vessel was 4:1, what was the quantity of kerosene added in the vessel?
  A. 1 litre
  B. 2 litre
  C. 5 litre
  D. 3 litre
  E. None of the Above
  Answer & Explanation

  Answer – E. None of the Above
  Explanation :
  Total quantity of the mixture = 18+80 = 98 litre
  quantity of petrol remaining = 18/2 = 9
  quantity of kerosene remaining = 80/2 = 40
  (40 + 2x) / (9 + x) = 4 / 1
  x = 2
  Quantity of kerosene added in the vessel = 2x = 4 litre
• A vessel which contains a mixture of acid and water in ratio 13:4. 25.5 litres of mixture is taken out from the vessel and 2.5 litres of pure water and 5 litres of acid is added to the mixture. If resultant mixture contains 25% water, what was the initial quantity of mixture in the vessel before the replacement in litres?
  A. 58 litre
  B. 68 litre
  C. 78 litre
  D. 48 litre
  E. None of the Above
  Answer & Explanation

  Answer – B. 68 litre
  Explanation :
  Quantity of Acid = 13x
  Quantity of water = 4x
  Total = 17x
  Resultant Mixture = 17x – 25.5 + 2.5 + 5 = 17x – 18
  Resultant water = 4x – 25.5 * (4/17) + 2.5 = 4x – 3.5
  Resultant mixture contains 25% water
  (17x – 18)*25/100 = 4x – 3.5
  x = 4
  Initial quantity = 17*4 = 68