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

Question : 1 [SSC MTS 2013]

The ratio in which a man must mix rice at Rs.10.20 per kg and Rs.14.40 per kg so as to make a mixture worth Rs.12.60 per kg, is

a) 18 : 24

b) 3 : 4

c) 2 : 5

d) 4 : 3

Answer: (b)

Required ratio = 1.8 : 2.4

= 18 : 24 = 3 : 4

Question : 2 [SSC CPO S.I.2007]

The milk and water in a mixture are in the ratio 7 : 5. When 15 litres of water are added to it, the ratio of milk and water in the new mixture becomes 7 : 8. The total quantity of water in the new mixture is

a) 60 litres

b) 96 litres

c) 40 litres

d) 35 litres

Answer: (c)

Let the quantity of milk in the mixture = 7x litres and that of water = 5x litres.

According to the question,

${7x}/{5x + 15} = 7/8$

56x = 35x + 105

56 x - 35 x = 105

21x = 105

$x = 105/21$ =5

Required quantity of water

= (5x + 15) litres

= 5 × 5 + 15 = 40 litres

Question : 3 [SSC CGL Prelim 2002]

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.

Question : 4 [SSC CPO S.I.2003]

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 : 5 [SSC CGL Prelim 2002]

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.

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