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 : 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) $1/4$

The correct answers to the above question in:

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

Question : 1

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 : 2

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 : 3

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

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.

Question : 4

In 30 litres mixture of acid, the ratio of acid and water is 2 : 3 . What amount of water should be added to the mixture so that the ratio of acid and water becomes 2 : 5 ?

a) 18 litres

b) 12 litres

c) 15 litres

d) 10 litres

Answer: (b)

In 30 litres of mixture,

Acid = $2/5 × 30$ = 12 litres

Water = $3/5 × 100$ = 18 litres

$12/{18 + x} = 2/5$

60 = 36 + 2x

2x = 60 - 36 = 24

x = 12 litres of water.

Question : 5

A mixture of 30 litres contain milk and water in the ratio of 7 : 3. How much water should be added to it so that the ratio of milk and water becomes 3 : 7 ?

a) 56 litres

b) 63 litres

c) 49 litres

d) 40 litres

Answer: (d)

Quantity of milk in 30 litre mixture

= $30/10 × 7$ = 21litres

Quantity of water

= $30/10 × 3 =9$ litres

Suppose x litres more water is added.

According to question,

$21/{9 + x} = 3/7$

9 + x = 49

x = 40 litres

Question : 6

Zinc and copper are in the ratio of 5 : 3 in 200 gm of an alloy. How much grams of copper be added to make the ratio as 3 : 5?

a) 72

b) 66

c) $1/200$

d) 133$1/3$

Answer: (d)

Weight of zinc

= $200 × 5/8$= 125 gram

Weight of copper

= $200 × 3/8$ = 75 gram.

Let the ratio of 125 gram zinc and x gram copper be 3 : 5

= $125/x = 3/5$

$x = {125× 5}/3 = 625/3$ gram

Addition of copper in mixture

= $625/3 - 75 = {625 - 225}/3$

= $400/3 = 133{1}/3$ gram.

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