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 : Zinc and copper are in the ratio 5 : 3 in 400 gm of an alloy. How much of copper (in grams) should be added to make the ratio 5 : 4?

(a) 72

(b) 200

(c) 66

(d) 50

The correct answers to the above question in:

Answer: (d)

In 400 gm of alloy,

Zinc = $5/8 × 400$ = 250 gm.

Copper = $3/8 × 400 = 150$ gm.

If x gm of copper be mixed, then

$250/{150 + x} = 5/4$

750 + 5x = 1000

5x = 1000 - 750 = 250

x = 50 gm.

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Read more alligation and mixtures problems Based Quantitative Aptitude Questions and Answers

Question : 1

The ratio of copper and zinc in brass is 13 : 7. How much zinc will be there in 100 kg of brass ?

a) 35 kg.

b) 40 kg.

c) 55 kg.

d) 20 kg.

Answer: (a)

In 20 gm of brass, quantity of zinc = 7gm

In 100 gm of brass, quantity of zinc = 7 × 5 = 35 gm.

Question : 2

In a mixture of 75 litres, the ratio of milk to water is 2 : 1. The amount of water to be further added to the mixture so as to make the ratio of the milk to water 1 : 2 will be

a) 75 litres

b) 80 litres

c) 60 litres

d) 45 litres

Answer: (a)

In 75 litres of the mixture,

Milk = $2/3$ × 75 = 50 litres

Water = $1/3 × 75$ = 25 litres

Let x litres of water be added.

Then, $50/{x + 25} = 1/2$

x + 25 = 100

x = 75 litres

Question : 3

In two alloys A and B, the ratio of zinc to tin is 5 : 2 and 3 : 4 respectively. Seven kg of the alloy A and 21 kg of the alloy B are mixed together to form a new alloy. What will be the ratio of zinc and tin in the new alloy ?

a) 2 : 3

b) 1 : 1

c) 1 : 2

d) 2 : 1

Answer: (b)

In 7 kg of alloy A,

Zinc = 5 kg, Tin = 2 kg

In 21 kg of alloy B

Zinc = ${21 × 3}/7 = 9$ kg

Tin = ${21 × 4}/7 = 12$ kg

Required ratio

= (5 + 9) : (2 + 12)

= 14 : 14 or 1 : 1

Question : 4

The proportion of acid and water in three samples is 2 : 1, 3 : 2 and 5 : 3. A mixture containing equal quantities of all three samples is made. The ratio of water and acid in the mixture is :

a) 227 : 120

b) 133 : 227

c) 227 : 133

d) 120 : 133

Answer: (c)

Required ratio

= $(2/3 + 3/5 + 5/8) : (1/3 + 2/5 + 3/8)$

= $({80 + 72 + 75}/120) : ({40 + 48 + 45}/120)$

= 227 : 133

Question : 5

In an alloy, the ratio of copper and zinc is 5 : 2. If 1.250 kg of zinc is mixed in 17 kg 500 g of alloy, then the ratio of copper and zinc will be

a) 3 : 2

b) 1 : 2

c) 2 : 3

d) 2 : 1

Answer: (d)

Weight of copper in 17kg 500 gm

i.e. 17500 gm of alloy

= $5/7$ × 17500 = 12500 gm

Weight of zinc = (17500 - 12500) = 5000 gm

1250 gm of zinc is mixed in alloy.

Total weight of zinc

= 1250 + 5000 = 6250 gm.

Required ratio

= 12500 : 6250 = 2 : 1

Question : 6

A barrel contains a mixture of wine and water in the ratio 3 : 1. How much fraction of the mixture must be drawn off and substituted by water so that the ratio of wine and water in the resultant mixture in the barrel becomes 1 : 1 ?

a) $3/4$

b) $2/3$

c) $1/3$

d) $1/4$

Answer: (c)

Let the barrel contain 4 litres of mixture.

Wine = 3 litres

Water = 1 litre

Let x litre mixture is taken out.

Wine in (4 - x) litres mixture

= $3/4(4 - x)$

On adding x litres water, water in mixture

= $(4 - x) × 1/4 + x = 1 - x/4 + x$

= ${4 - x +4x}/4 = {4 + 3x}/4$

$3/4(4 - x) = {4 + 3x}/4$

$3 - {3x}/4 = 1 + {3x}/4$

$2 = {6x}/4$

$x = {2 × 4}/6 = 4/3$

Required answer

= ${4/3}/4 = 1/3$

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