Mixtures and Alligations Questions for SSC-CGL
Download SSC CGL Mixtures and Alligations Questions with answers PDF based on previous papers very useful for SSC CGL exams. Very important Mixtures and Alligations questions for SSC exams.
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Question 1: The ratio of spirit and water is 2 : 5. If the volume of solution is increased by 50% by adding spirit only. What is the resultant ratio of spirit and water?
a) 9 : 10
b) 12 : 15
c) 11 : 10
d) 3 : 4
Question 2: A solution of milk and water contains milk and water in the ratio of 3 : 2. Another solution of milk and water contains milk and water in the ratio of 2 : 1. 40 liters of the first solution is mixed with 30 liter of the second solution. The ratio of milk and water in the resultant solution is:
a) 22:13
b) 13:22
c) 6:5
d) 5:6
Question 3: In a mixture of 60 L, the ratio of milk and water is 2:3, then the quantity of water in the mixture is:
a) 20 L
b) 45 L
c) 36 L
d) 16 L
Question 4: Two alloys A and B contain copper and zinc in the ratio 7 : 2 and 5 : 3 respectively. How many kg of A and B must be melted in order to get an alloy of 44 kg containing copper and Zinc in the ratio 3 : 1?
a) 24 kg, 20 kg
b) 30 kg, 14 kg
c) 28 kg, 16 kg
d) 36 kg, 8 kg
Question 5: Two solutions of acid and water containing acid and water in the ratio 2 : 7 and 4 : 5, respectively are mixed in the ratio 2 : 5. What is the ratio of acid and water in the resulting solution?
a) 8 : 13
b) 3 : 7
c) 8 : 17
d) 2 : 1
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Question 6: In what proportion must a grocer mix one kind of bajra at ₹ 45 per kg with another at ₹ 32 per kg in order that by selling the mixture at ₹ 48 per kg he may make a profit of 20%?
a) 4 : 1
b) 8 : 5
c) 7 : 5
d) 9 : 5
Question 7: Two bottles A and B contain diluted acid. In bottle A, the amount of water is double the amount of acid while in bottle B, the amount of acid is 3 times that of water. How much mixture(in litres) should be taken from each bottle A and B respectively in order to prepare 5 liters diluted acid containing equal amount of acid and water?
a) 1,4
b) 4,1
c) 2,3
d) 3,2
Question 8: In what ratio should coffee powder costing Rs 2500/kg be mixed with coffee powder costing Rs 1500/kg so that the cost of the mixture is Rs 2250/kg?
a) 1 : 4
b) 4 : 1
c) 3 : 1
d) 1 : 3
Question 9: Solution A contains 10% acid and solution B contains 30% acid. In what ratio should solution A be mixed with Solution B to obtain a mixture with 25% acid?
a) 1 : 2
b) 3 : 1
c) 1 : 3
d) 2 : 1
Question 10: Three bottles of equal capacity are containing a mixture of milk and water in ratio 2 : 1, 3 : 7 and 4 : 11 respectively. These three bottles are emptied into a large bottle. What is the ratio of milk and water respectively in this large bottle?
a) 37 : 53
b) 37 : 90
c) 37 : 30
d) 7 : 30
Question 11: In what ratio wheat at Rs 32/kg should be mixed with wheat at Rs 24/kg so that on selling the mixture at Rs 39/kg there is a profit of 30%?
a) 3 : 1
b) 2 : 3
c) 1 : 4
d) 2 : 5
Question 12: 20 liters of a mixture contains milk and water in the ratio 3 : 1. Then the amount of milk to be added to the mixture so as to have milk and water in the ratio 4 :1 is
a) 6 liters
b) 5 liters
c) 4 liters
d) 7 liters
Question 13: A mixture contains milk and water in the ratio 5 : 1. On adding 5 litres of water, the ratio of milk and water becomes 5 : 2. The quantity of milk in the mixture is
a) 25 litres
b) 16 litres
c) 22.75 litres
d) 32.5 litres
Question 14: Two vessels contain mixture of petrol and kerosene in the ratio 4 : 3 and 3 : 5 respectively. The ratio of the volumes of the quantities from the two vessels to be mixed together so that the new mixture may contain same volume of petrol and kerosene is
a) 9 : 6
b) 8 : 2
c) 7 : 8
d) 7 : 4
Question 15: In a mixture, sugar and milk are in the ratio 4 : 5. If 7 litres of milk is added to it, then the ratio of sugar and milk in the new mixture becomes 2 : 3. What is the total quantity (In litres) of sugar in new mixture?
a) 35
b) 28
c) 42
d) 24
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Answers & Solutions:
1) Answer (C)
Let the spirit and water content be 2x and 5x
Total quantity =7x
Half of 7x=3.5x
So 3.5x of spirit is added to it.
Total spirit=2x+3.5x
Total water=5x
Ratio=10:11
2) Answer (A)
Ratio of milk to water in solution 1 is 3:2
Solution 1 contains 40 liters.
Milk content in solution 1 =(3/5)*40
=24 liters
Water content=40-24=16 liters
Ratio of milk to water in solution 2 is 2:1
Solution 2 contains 30 liters.
Milk content in solution 2 =(2/3)*30
=20 liters
Water content=30-20=10 liters
Total milk content=24+20=44 liters
Total water content =16+10=26 liters
Ratio=22:13
3) Answer (C)
Let the milk and water content be 2x and 3x
Total content=60 liters
Sum=5x
Therefore 5x=60
x=12
Water =3*12
=36 liters
4) Answer (D)
Copper in the A alloy=7/9
Copper in the B alloy=5/8
Copper in the resultant mixture=3/4
let the ratio in which they are mixed is x
By using the principle of allegation we have
x=((3/4)-(5/8))/((7/9)-(3/4))
x=(1/8)/(1/36)
x=9:2
Given 44 kg of mixture and so zinc copper present is (3/4)*44=33 kg
Therefore (7/9)*9y +(5/8)*2y =33
7y+(5y/4)=33
33y/4 =33
y=4
9y=36 kgs and 2y=8 kgs
5) Answer (A)
acid content in 1st solution 2/9
acid content in second solution=4/9
They are mixed in the ratio 2:5
x is the acid present in the final mixture
By using the principle of allegations we have
((4/9)-x)/(x-(2/9))=2/5
(20/9)-5x=2x-(4/9)
7x=24/9
x=8/21
8 parts of acid and 13 parts of water.
Ratio=8/13
6) Answer (B)
Cost Price of one kind of Bajra = Rs.45 per kg
Cost Price of another kind of Bajra = Rs.32 per kg
Given, Selling Price = Rs.48 per kg
Profit = 20%
Then, Cost Price = $\dfrac{100}{120}\times48 = Rs.40$ per kg
Therefore, Required ratio in which the two types of Bajra are to be mixed is 8 : 5.
7) Answer (D)
Acid : Water in Bottle A = 1 : 2
Acid in Bottle A = $\dfrac{1}{3}$
Acid : Water in Bottle B = 3 : 1
Acid in Bottle B = $\dfrac{3}{4}$
Acid : Water in Required solution = 1 : 1
Acid in required solution = $\dfrac{1}{2}$
Therefore, Required ratio = $\dfrac{1}{4} : \dfrac{1}{6} = 6 : 4 = 3 : 2$
8) Answer (C)
Given 2500 per kg and 1500 per kg
resultant is 2250 per kg
By applying the rule of allegation require ratio =(2250-1500)/(2500-2250)
=750:250
=3:1
9) Answer (C)
In solution 1 acid percent=10
In solution 2 acid percent=30
In the resulting mixture acid percent=25%
By applying the principle of allegations we have
=(30-25)/(25-10)
=5/15
=1:3
10) Answer (A)
Let capacity of each bottle = L.C.M.(3,10,15) = 30 litres
=> Milk in first bottle = $\frac{2}{2+1}\times30=20$ litres
and water in first bottle = $30-20=10$ litres
Similarly, in 2nd bottle, milk = 9 litres and water = 21 litres
In 3rd bottle, milk = 8 litres and water = 22 litres
=> Total quantity of milk = $20+9+8=37$ litres
and water = $10+21+22=53$ litres
$\therefore$ Required ratio = 37 : 53
=> Ans – (A)
11) Answer (A)
Selling price of mixture after 30% profit = Rs. 39/kg
=> Cost price of mixture = $39\times\frac{100}{130}=Rs.$ $30$ per kg
Let ratio in which wheat at Rs 32/kg should be mixed with wheat at Rs 24/kg = $x:y$
According to ques,
=> $32x+24y=30(x+y)$
=> $32x+24y=30x+30y$
=> $32x-30x=30y-24y$
=> $2x=6y$
=> $\frac{x}{y}=\frac{6}{2}=\frac{3}{1}$
$\therefore$ Ratio in which wheat at Rs 32/kg should be mixed with wheat at Rs 24/kg = 3 : 1
=> Ans – (A)
12) Answer (B)
Ratio of milk and water in 20 litres mixture = 3:1
=> Quantity of milk = $\frac{3}{(3+1)}\times20=15$ litres
=> Quantity of water = $20-15=5$ litres
Let amount of milk added = $x$ litres
According to ques,
=> $\frac{15+x}{5}=\frac{4}{1}$
=> $15+x=20$
=> $x=20-15=5$
$\therefore$ The amount of milk to be added to the mixture so as to have milk and water in the ratio 4 :1 = 5 litres
=> Ans – (B)
13) Answer (A)
Let quantity of water in mixture = $x$ litres, => Quantity of milk = $5x$ litres
According to ques, => $\frac{5x}{x+5}=\frac{5}{2}$
=> $\frac{x}{x+5}=\frac{1}{2}$
=> $2x=x+5$
=> $2x-x=5$
=> $x=5$
$\therefore$ Quantity of milk = $5\times5=25$ litres
=> Ans – (A)
14) Answer (D)
Ratio of petrol and whole mixture in 1st vessel = $\frac{4}{7}$
Ratio of petrol and whole mixture in 2nd vessel = $\frac{3}{8}$
Also, ratio of petrol and whole mixture in the final mixture = $\frac{1}{2}$
By alligation method,
=> Petrol : Kerosene = $\frac{1}{8}:\frac{1}{14}=14:8$
= $7:4$
=> Ans – (D)
15) Answer (B)
Let quantity of milk and sugar be $4x$ and $5x$ litres respectively.
According to ques,
=> $\frac{4x}{5x+7}=\frac{2}{3}$
=> $12x=10x+14$
=> $12x-10x=2x=14$
=> $x=\frac{14}{2}=7$
$\therefore$ Total quantity of sugar = $4\times7=28$ litres
=> Ans – (B)
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