type 8 alligation & mixtures based ratio & proportion problems Practice Questions Answers Test with Solutions & More Shortcuts

Question : 11 [SSC CGL Prelim 2008]

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 : 12 [SSCCHSL 2013]

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 : 13 [SSC Delhi Police S.I.2012]

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) $1/3$

Answer: (a)

Ratio = 4 : 1

Required quantity = $1/5$

Question : 14 [SSC CHSL 2012]

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 : 15 [SSC CGL Prelim 2004]

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

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