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 vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup ?

(a) $1/5$

(b) $1/7$

(c) $1/4$

(d) $1/3$

The correct answers to the above question in:

Answer: (a)

Ratio = 4 : 1

Required quantity = $1/5$

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

Question : 1

Two vessels A and B contain milk and water mixed in the ratio 8 : 5 and 5 : 2 respectively. The ratio in which these two mixtures be mixed to get a new mixture containing 69$3/13$% milk is:

a) 5 : 7

b) 2 : 7

c) 5 : 2

d) 3 : 5

Answer: (b)

Milk in the resulting mixture = $9/13$

= ${65 - 63}/{7 × 13} = 2/{7 × 13}$

Required ratio

= $2/{7 × 13} : 1/13$ = 2 : 7

Question : 2

There are three containers of equal capacity. The ratio of Sulphuric acid to water in the first container is 3 : 2, that in the second container is 7 : 3 and in the third container it is 11 : 4. If all the liquids are mixed together, then the ratio of Sulphuric acid to water in the mixture will be :

a) 60 : 29

b) 59 : 29

c) 61 : 28

d) 61 : 29

Answer: (d)

In the new vessel, we have.

Sulphuric acid

= $3/5 + 7/10 + 11/15$

=${18 + 21 + 22}/30 = 61/30$

Water = $2/5 + 3/10 + 4/15$

= ${12 + 9 + 8}/30 = 29/30$

Sulphuric acid : Water

= $61/30 : 29/30$= 61 : 29

Question : 3

A can contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. Litres of liquid A contained by the can initially was

a) 21

b) 25

c) 20

d) 10

Answer: (a)

Let A = 7x litre, B = 5x litre

In 9 litres of mixture,

A = ${7x}/{12x} × 9 = 21/4$ litres

B = ${5x}/{12x} × 9 = 15/4$ litres

In new situation,

${7x - 21/4}/{5x - 15/4 + 9} = 7/9$

${28x - 21}/{20x - 15 + 36} = 7/9$

252x - 189 = 140x + 147

112x = 336

x = 3

Initial quantity of liquid A

= 7x = 7 × 3 = 21 litres

Question : 4

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 : 5

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 : 6

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.

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