type 8 alligation & mixtures based ratio & proportion problems Section-Wise Topic Notes With Detailed Explanation And Example Questions
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The following question based on ratio & proportion topic of quantitative aptitude
(a) 6$2/3$
(b) 6$3/4$
(c) 6$1/2$
(d) 6
The correct answers to the above question in:
Answer: (a)
In 40 litres mixture,
Quantity of milk
= $7/8$ × 40 = 35 litres
Quantity of water = 5 litres
Let x litres of water be mixed
$35/{5 + x} =3/1$
3x + 15 = 35
3x = 20
$x = 20/3 = 6{2}/3$ litres
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Read more alligation and mixtures problems Based Quantitative Aptitude Questions and Answers
Question : 1
A jar contained a mixture of two liquids A and B in the ratio 4 : 1. When 10 litres of the mixture was taken out and 10 litres of liquid B was poured into the jar, this ratio became 2 : 3. The quantity of liquid A contained in the jar initially was
a) 16 litres
b) 40 litres
c) 8 litres
d) 4 litres
Answer »Answer: (b)
Let the initial quantity of liquids A and B in the jar be 4x and x litres respectively.
After taking out 10 litres of the mixture,
Liquid A
= $4x - 4/5 × 10 = (4x - 8)$ litres
Liquid B
= $4x - 1/5 ×10 = (4x - 2)$ litres
After pouring 10 litres of liquid B,
${4x - 8}/{4x - 2 + 10} = 2/3$
12x - 24 = 8x + 16
4x = 40
$x = 40/4$ = 10
Quantity of liquid A = 4x
= 4 × 10 = 40 litres
Question : 2
A and B are two alloys of gold and copper prepared by mixing metals in ratios 7 : 2 and 7 : 11 respectively. If equal quantities of the alloys are melted to form a third alloy C, the ratio of gold and copper in C will be ;
a) 9 : 5
b) 5 : 7
c) 5 : 9
d) 7 : 5
Answer »Answer: (d)
Gold = $7/9 : 7/18 = 14/18 : 7/18$
Gold in new mixture
= 14 + 7 = 21
and copper = 18 × 2 - 21
= 36 - 21 = 15
Required ratio
= 21 : 15 = 7 : 5
Question : 3
Vessels A and B contain mixtures of milk and water in the ratios 4 : 5 and 5 : 1 respectively. In what ratio should quantities of mixture be taken from A and B to form a mixture in which milk to water is in the ratio 5 : 4?
a) 5 : 2
b) 2 : 3
c) 4 : 3
d) 2 : 5
Answer »Answer: (a)
First of all we write the fraction of milk present in three mixtures.
In A; $4/9$ and In B; $5/6$
In combination of A and B; $5/9$
From alligation rule,
= $5/18 : 1/9$
$5/18 : 2/18$ ⇒ 5 : 2
So, ratio of
A : B = 5 : 2
Question : 4
In 80 litres mixture of milk and water the ratio of amount of milk to that of amount of water is 7 : 3. In order to make this ratio 2 : 1, how many litres of water should be added ?
a) 8
b) 4
c) 6
d) 5
Answer »Answer: (b)
Quantity of milk
= $7/10 × 80 = 56$ litres
Quantity of water
= $3/10 × 80$ = 24 litres
Let x litre water be added Then,
$56/{24 + x} = 2/1$
24 + x =28 ⇒ x = 4 litres
Question : 5
A mixture contains spirit and water in the ratio 3 : 2. If it contains 3 litres more spirit than water, the quantity of spirit in the mixture is
a) 8 litres
b) 9 litres
c) 12 litres
d) 10 litres
Answer »Answer: (b)
Let the amount of water be x litres.
Then, ${x + 3}/x = 3/2$
or 2x + 6 = 3x
or x = 6
The quantity of spirit in the mixture
= x + 3 = 6 + 3 = 9 litres
Question : 6
200 litres of a mixture contains milk and water in the ratio 17 : 3. After the addition of some more milk to it, the ratio of milk to water in the resulting mixture becomes 7 : 1. The quantity of milk added to it was
a) 60 litres
b) 80 litres
c) 40 litres
d) 20 litres
Answer »Answer: (c)
Let the quantity of additional milk added = x litres
In the mixture of 200 litres,
Quantity of milk
= $17/20 × 200$ = 170 litres
Quantity of water = 30 litres
According to the question,
${170 + x}/30 = 7/1$
170 + x = 210
x = 210 - 170 = 40 litres
GET ratio & proportion PRACTICE TEST EXERCISES
type 1 basic concepts of ratio & proportion
type 2 age based ratio & proportion problems
type 3 addition subtraction product on ratio & proportion
type 4 income & expenditure based ratio & proportion problems
type 5 shares & partnership based ratio & proportion problems
type 6 fractions based ratio & proportion problems
type 7 finding sum difference product based ratio & proportion problems
type 8 alligation & mixtures based ratio & proportion problems
type 9 coins & rupees based ratio & proportion problems
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