Alligation & Mixtures Model Questions Set 1 Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 1 EXERCISES
The following question based on Alligation & Mixtures topic of quantitative aptitude
(a) 101 : 49
(b) 131 : 69
(c) 181 : 49
(d) 121 : 59
e) None of these
The correct answers to the above question in:
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
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Question : 1
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
Question : 2
A mixture of certain quantity of milk with 16 litres of water is worth 90 P per litre. If pure milk be worth Rs. 1.08 per litre, how much milk is there in the mixture?
a) 70
b) 90
c) 60
d) 80
e) None of these
Answer »Answer: (d)
The mean value is 90 P and the price of water is 0 P.
![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-3-1.png)
By the Alligation Rule, Milk and water are in the ratio of 5 : 1.
∴ quantity of milk in the mixture = 5 × 16 = 80 litres.
Question : 3
A person has a chemical of Rs. 25 per litre. In what ratio should water be mixed in that chemical so that after selling the mixture at Rs. 20/litre he may get a profit of 25%?
a) 15
b) 17
c) 14
d) 16
e) None of these
Answer »Answer: (d)
In this question, the alligation method is applicable on prices,
so we should get the average price of mixture.
SP of mixture = Rs.20/litre; profit = 25%
∴ average price = 20 × ${100}/{125}$ = Rs. 16/litre
Question : 4
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 : 5
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 : 6
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
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