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

Question : 16 [SSC CGL Tier-1 2011]

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 : 17 [SSC CHSL 2011]

A container contains two liquids A and B in the ratio 7 : 5. When 9 litres of mixture are drawn off and the container is filled with B, the ratio of A and B becomes 1:1. How many litres of liquid A was in the container initially ?

a) 36$3/4$

b) 26$3/4$

c) 16$1/2$

d) 26

Answer: (a)

Let Liquid A = 7x litres

Liquid B = 5x litres

In 9 litres,

A = $7/12 × 9 = 21/4$ litres

B = $5/12 × 9 = 15/4$ litres

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

$2x = 21/4 - 15/4 + 9$

$2x = {21 - 15 + 36}/4 =42/4$

$x = 21/4$

Liquid A = $7 × 21/4$

= $147/4 = 36{3}/4$ litre

Question : 18 [SSC CHSL 2013]

A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the mixture, the ratio becomes 4 : 5. The quantity of alcohol in the given mixture is

a) 15 litres

b) 10 litres

c) 4 litres

d) 3 litres

Answer: (b)

In original mixture,

Alcohol = 4x litres

Water = 3x litres

On adding 5 litres of water,

${4x}/{3x + 5} = 4/5$

20x = 12x + 20

8x = 20

$x = 20/8 = 5/2$

Quantity of alcohol

= $4x = 4 × 5/2$ = 10 litres

Question : 19 [SSC CHSL 2013]

Two alloys are both made up of copper and tin. The ratio of copper and tin in the first alloy is 1 : 3 and in the second alloy is 2 : 5. In what ratio should the two alloys be mixed to obtain a new alloy in which the ratio of tin and copper be 8 : 3 ?

a) 3 : 8

b) 5 : 11

c) 4 : 7

d) 3 : 5

Answer: (c)

By rule of alligation

Required ratio

= $1/77 : 1/44$ = 4 7

Question : 20 [SSC CHSL 2012]

A container contains 60 kg of milk. From this container 6 kg of milk was taken out and replaced by water. This process was repeated further two times. The amount of milk left in the container is

a) 43.74 kg

b) 47.6 kg

c) 39.64 kg

d) 34.24 kg

Answer: (a)

Amount of milk left

= Initial amount ×

$(1-\text”Amount taken out in each operation”/\text”Initial amount”)^3$

= $60(1 - 6/60)^3$

= $60(1 - 1/10)^3$

= $60 × 9/10 × 9/10 × 9/10$

= 43.74 kg.

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