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

Question : 26 [SSC CHSL 2012]

A and B are two alloys of gold and copper prepared by mixing metals in ratios 7 : 2 and 7 : 11 respectively. If equal quantities of the alloys are melted to form a third alloy C, the ratio of gold and copper in C will be ;

a) 9 : 5

b) 5 : 7

c) 5 : 9

d) 7 : 5

Answer: (d)

Gold = $7/9 : 7/18 = 14/18 : 7/18$

Gold in new mixture

= 14 + 7 = 21

and copper = 18 × 2 - 21

= 36 - 21 = 15

Required ratio

= 21 : 15 = 7 : 5

Question : 27 [SSC SO 2006]

Vessels A and B contain mixtures of milk and water in the ratios 4 : 5 and 5 : 1 respectively. In what ratio should quantities of mixture be taken from A and B to form a mixture in which milk to water is in the ratio 5 : 4?

a) 5 : 2

b) 2 : 3

c) 4 : 3

d) 2 : 5

Answer: (a)

First of all we write the fraction of milk present in three mixtures.

In A; $4/9$ and In B; $5/6$

In combination of A and B; $5/9$

From alligation rule,

= $5/18 : 1/9$

$5/18 : 2/18$ ⇒ 5 : 2

So, ratio of

A : B = 5 : 2

Question : 28 [SSC MTS 2011]

Two vessels A and B contain milk and water mixed in the ratio 4 : 3 and 2 : 3. The ratio in which these mixtures be mixed to form a new mixture containing half milk and half water is

a) 5 : 6

b) 4 : 3

c) 6 : 5

d) 7 : 5

Answer: (d)

Required ratio

= $1/10 : 1/14$ = 7 : 5

Question : 29 [SSC SO 2005]

There is 81 litres pure milk in a container. One-third of milk is replaced by water in the container. Again one-third of mixture is extracted and equal amount of water is added. What is the ratio of milk to water in the new mixture?

a) 2 : 1

b) 4 : 5

c) 1 : 1

d) 1 : 2

Answer: (b)

Quantity of milk in the last

= $81(1 - 27/81)^2 = 81(1 - 1/3)^2$

= $81 × 2/3 × 2/3$ = 36

Quantity of water in the last

= 81 - 36 = 45

Ratio = $36/45 = 4/5 = 4 : 5$

Question : 30 [SSC CGL Prelim 2008]

In a 729 litres mixture of milk and water, the ratio of milk to water is 7 : 2. To get a new mixture containing milk and water in the ratio 7 : 3, the amount of water to be added is

a) 56 litres

b) 50 litres

c) 71 litres

d) 81 litres

Answer: (d)

Quantity of milk in 729 litres of mixture

= $7/9 × 729$ = 567 litres

Quantity of water

= (729 - 567) litres = 162 litres.

Let x litres of water is mixed to get the required ratio of 7 : 3

$567/{162 + x} =7/3$

7x + 1134 = 1701

7x = 1701 - 1134 = 567

$x = 567/7$ = 81 litres

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