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

Questions : 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

The correct answers to the above question in:

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

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Question : 1

In 40 litres mixture of milk and water the ratio of milk to water is 7 : 1. In order to make the ratio of milk and water 3 : 1, the quantity of water (in litres) that should be added to the mixture will be

a) 6$2/3$

b) 6$3/4$

c) 6$1/2$

d) 6

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

Question : 2

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: (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 : 3

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: (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 : 4

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: (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 : 5

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: (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

Question : 6

A container contains 60 kg of milk. From this container 6 kg of milk was taken out and replaced by water. This process was repeated further two times. The amount of milk left in the container is

a) 43.74 kg

b) 47.6 kg

c) 39.64 kg

d) 34.24 kg

Answer: (a)

Amount of milk left

= Initial amount ×

$(1-\text”Amount taken out in each operation”/\text”Initial amount”)^3$

= $60(1 - 6/60)^3$

= $60(1 - 1/10)^3$

= $60 × 9/10 × 9/10 × 9/10$

= 43.74 kg.

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