Alligation & Mixtures Model Questions Set 1 Practice Questions Answers Test With Solutions & More Shortcuts
ALLIGATION & MIXTURES PRACTICE TEST [1 - EXERCISES]
Alligation & Mixtures Model Questions Set 1
Question : 16
In what ratio must a grocer mix two varieties of tea worth Rs. 60 a kg and Rs. 65 a kg so that by selling the mixture at Rs. 68.20 a kg he may gain 10%?
a) 3 : 4
b) 4 : 5
c) 3 : 2
d) 3 : 5
e) None of these
Answer »Answer: (c)
S.P. of 1 kg of the mixture = Rs. 68.20, Gain = 10%
C.P. of 1 kg of the mixture = Rs. $({100}/{110} × 68.20)$ = Rs. 62.
By the rule of alligation, we have
![alligations-and-mixtures-mcq-problems-competitive-exams-quantitative-aptitude alligations-and-mixtures-mcq-problems-competitive-exams-quantitative-aptitude](https://careericons.com/adminicon/bunch/images/alligations-and-mixtures-mcq-problems-competitive-exams-3-26.png)
∴ Required ratio = 3 : 2
Question : 17
How much water must be added to a cask which contains 40 litres of milk at cost price Rs. 3.5/litres so that the cost of milk reduces to Rs. 2/litre?
a) 35
b) 50
c) 20
d) 45
e) None of these
Answer »Answer: (e)
This question can be solved in so many different ways. But the method of alligation method is the simplest of all the methods. We will apply the alligation on price of milk, water and mixture.
![alligations-and-mixtures-mcq-problems-competitive-exams-quantitative-aptitude alligations-and-mixtures-mcq-problems-competitive-exams-quantitative-aptitude](https://careericons.com/adminicon/bunch/images/alligations-and-mixtures-mcq-problems-competitive-exams-3-11.png)
∴ ratio of milk and water should be 2 : 15 = 4 : 3
∴ added water = ${40}/4$ × 3 = 30 litres
Question : 18
In a mixture of 60 litres, the ratio of milk to water is 2 : 1. If the ratio of milk to water is to be 1 : 2, then amount of water to be further added is ___________.
a) 40
b) 80
c) 20
d) 60
e) None of these
Answer »Answer: (d)
Apply the alligation on fraction of milk in each mixture.
![alligations-and-mixtures-mcq-problems-competitive-exams-quantitative-aptitude alligations-and-mixtures-mcq-problems-competitive-exams-quantitative-aptitude](https://careericons.com/adminicon/bunch/images/alligations-and-mixtures-mcq-problems-competitive-exams-3-14.png)
Ratio of mixture to water = 1 : 1
Therefore, if there is 60 liture of solution, 60 litres of water should be added.
Question : 19
In three vessels each of 10 litres capacity, mixture of milk and water is filled. The ratios of milk and water are 2 : 1, 3 : 1 and 3 : 2 in the three respective vessels. If all the three vessels are emptied into a single large vessel, find the proportion of milk and water in the mixture.
a) 101 : 49
b) 131 : 69
c) 181 : 49
d) 121 : 59
e) None of these
Answer »Answer: (d)
By the above theorem the required ratio is
$({2/{2+1}}+{3/{3+1}}+{3/{3+2}}):({1/{2+1}}+{1/{3+1}}+{2/{3+2}})$
= $({2/3}+{3/4}+{3/5}):({1/3}+{1/4}+{2/5})$
= ${40 + 45 + 36}/{3 × 4 × 5} : {20 + 15 + 24}/{3 × 4 × 5}$ = 121 : 59
Question : 20
Two vessels A and B contain milk and water mixed in the ratio 8 : 5 and 5 : 2 respectively. The ratio in which these two mixtures be mixed to get a new mixture containing 69$3/13$% milk, is :
a) 3 : 5
b) 5 : 7
c) 2 : 7
d) 5 : 2
e) None of these
Answer »Answer: (c)
Let cost of 1 litre milk be Re. 1.
Milk in 1 litre mix. in B = $8/{13}$ litre, C.P. of a litre mix. in
B = Re. $5/7$.
Milk in 1 litre mix. in B = $5/7$ litre, C.P. of 1 litre mix. in
B = Re. $5/7$
Milk in 1 litre of final mix. = $({{900}/13} × {1/{100}} × 1) = 9/{13}$ litre;
mean price = Re. $9/{13}$
By the rule of alligation, we have:
![alligations-and-mixtures-mcq-problems-competitive-exams-quantitative-aptitude alligations-and-mixtures-mcq-problems-competitive-exams-quantitative-aptitude](https://careericons.com/adminicon/bunch/images/alligations-and-mixtures-mcq-problems-competitive-exams-3-29.png)
∴ Required ratio = $2/{91} : 1/{13}$ = 2 : 7
IMPORTANT QUANTITATIVE APTITUDE EXERCISES
Alligation & Mixtures Model Questions Set 1 Online Quiz
Click to Start..QUANTITATIVE APTITUDE CATEGORIES
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» Number System
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» Average
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» LCM & HCF
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» Percentage
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» Profit & Loss
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» Time & Work
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» Pipes & Cisterns
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» Time & Distance
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» Trains
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» Compound Interest
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» Simplification
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» Discount
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» Power
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» Permutations & Combination
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» Ratio & Proportion
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» Advance Math
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» Algebraic Expressions
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» Trigonometric Ratios & Identities
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» Simple Interest
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» Alligation & Mixtures
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» Boats & Streams
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» Set Theory
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» Linear Equations
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» Quadratic Equations
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» Mensuration
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» Squareroots & Cuberoots
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» Data Sufficiency
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» Logarithm
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» Probability
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» Statistics
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