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 : 21
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.
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 : 22
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 : 23
Milk and water are mixed in a vessel A in the proportion 5 : 2, and in vessel B in the proportion 8 : 5. In what proportion should quantities be taken from the two vessels so as to form a mixture in which milk and water will be in the proportion of 9 : 4?
a) 5 : 7
b) 7 : 9
c) 4 : 5
d) 7 : 2
e) None of these
Answer »Answer: (d)
In vessel A, milk = $5/7$ of the weight of mixture
In vessel B, milk = $8/{13}$ of the weight of mixture. Now, we
want to form a mixture in which milk will be $9/{13}$ of the weight of this mixture.
By alligation rule:
∴ required proportion is $1/{13} : 2/{91}$ = 7 : 2
Question : 24
300 gm of sugar solution has 40% sugar in it. How much sugar should be added to make it 50% in the solution?
a) 50 gm
b) 70 gm
c) 40 gm
d) 60 gm
e) None of these
Answer »Answer: (d)
The existing solution has 40% sugar. And sugar is to be mixed;
so the other solution has 100% sugar. So, by alligation method:
∴ The two mixtures should be added in the ratio 5 : 1.
Therefore, required sugar = ${300}/5$ × 1 = 60 gm
Question : 25
In what ratio must a person mix three kinds of wheat costing him Rs. 1.20, Rs. 1.44 and Rs. 1.74 per kg, so that the mixture may be worth Rs. 1.41 per kg?
a) 4 : 5 : 7
b) 13 : 7 : 9
c) 1 : 2 : 3
d) 12 : 7 : 7
e) None of these
Answer »Answer: (d)
1st wheat 120
2nd wheat 144 3rd wheat 174
following the above rule, we have, [(144 – 141) + (174 – 141)]
[= 141 – 120]
[= 141 – 120]
Therefore, the required ratio = 36 : 21 : 21 = 12 : 7 : 7
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