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

Question : 21 [SSC SO 2007]

200 litres of a mixture contains milk and water in the ratio 17 : 3. After the addition of some more milk to it, the ratio of milk to water in the resulting mixture becomes 7 : 1. The quantity of milk added to it was

a) 60 litres

b) 80 litres

c) 40 litres

d) 20 litres

Answer: (c)

Let the quantity of additional milk added = x litres

In the mixture of 200 litres,

Quantity of milk

= $17/20 × 200$ = 170 litres

Quantity of water = 30 litres

According to the question,

${170 + x}/30 = 7/1$

170 + x = 210

x = 210 - 170 = 40 litres

Question : 22 [SSC CGL Prelim 2003]

A mixture contains spirit and water in the ratio 3 : 2. If it contains 3 litres more spirit than water, the quantity of spirit in the mixture is

a) 8 litres

b) 9 litres

c) 12 litres

d) 10 litres

Answer: (b)

Let the amount of water be x litres.

Then, ${x + 3}/x = 3/2$

or 2x + 6 = 3x

or x = 6

The quantity of spirit in the mixture

= x + 3 = 6 + 3 = 9 litres

Question : 23 [SSC SO 2005]

In 80 litres mixture of milk and water the ratio of amount of milk to that of amount of water is 7 : 3. In order to make this ratio 2 : 1, how many litres of water should be added ?

a) 8

b) 4

c) 6

d) 5

Answer: (b)

Quantity of milk

= $7/10 × 80 = 56$ litres

Quantity of water

= $3/10 × 80$ = 24 litres

Let x litre water be added Then,

$56/{24 + x} = 2/1$

24 + x =28 ⇒ x = 4 litres

Question : 24 [SSC CGL Prelim 2008]

In 40 litres mixture of milk and water the ratio of milk to water is 7 : 1. In order to make the ratio of milk and water 3 : 1, the quantity of water (in litres) that should be added to the mixture will be

a) 6$2/3$

b) 6$3/4$

c) 6$1/2$

d) 6

Answer: (a)

In 40 litres mixture,

Quantity of milk

= $7/8$ × 40 = 35 litres

Quantity of water = 5 litres

Let x litres of water be mixed

$35/{5 + x} =3/1$

3x + 15 = 35

3x = 20

$x = 20/3 = 6{2}/3$ litres

Question : 25 [SSC CGL Prelim 2008]

A jar contained a mixture of two liquids A and B in the ratio 4 : 1. When 10 litres of the mixture was taken out and 10 litres of liquid B was poured into the jar, this ratio became 2 : 3. The quantity of liquid A contained in the jar initially was

a) 16 litres

b) 40 litres

c) 8 litres

d) 4 litres

Answer: (b)

Let the initial quantity of liquids A and B in the jar be 4x and x litres respectively.

After taking out 10 litres of the mixture,

Liquid A

= $4x - 4/5 × 10 = (4x - 8)$ litres

Liquid B

= $4x - 1/5 ×10 = (4x - 2)$ litres

After pouring 10 litres of liquid B,

${4x - 8}/{4x - 2 + 10} = 2/3$

12x - 24 = 8x + 16

4x = 40

$x = 40/4$ = 10

Quantity of liquid A = 4x

= 4 × 10 = 40 litres

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