__Allegations and Mixtures Practice Set - 1__**1. In a pot, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk, the pot would be full and ratio of milk and water would become 6 : 5. Find the capacity of the pot ?**

A) 11 litres

B) 22 litres

C) 33 litres

D) 44 litres

**2. A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained ?**

A) 5 : 3

B) 1 : 4

C) 4 : 1

D) 9 : 1

**3. A mixture of 70 litres of Fruit Juice and water contains 10% water. How many litres of water should be added to the mixture so that the mixture contains 12 1/2% water ?**

A) 2 lit

B) 4 lit

C) 1 lit

D) 3 it

E) 5 lit

**4. A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture ?**

A) 5 lit

B) 10 lit

C) 15 lit

D) 20 lit

E) 25 lit

**5. 640 ml of a mixture contains milk and water in ratio 6:2. How much of the water is to be added to get a new mixture containing half milk and half water ?**

A) 360 ml

B) 320 ml

C) 310 ml

D) 330 ml

E) 350 ml

**6. Equal quantities of three mixtures of milk and water are mixed in the ratio 1:2, 2:3 and 3:4. The ratio of water and milk in the mixture is ?**

A) 193 : 122

B) 97 : 102

C) 115 : 201

D) 147 : 185

E) 151 : 207

**7. In a mixture of milk and water the proportion of water by weight was 75%. If in 60 gm of mixture 15 gm water was added, what would be the percentage of water ? (Weight in gm)**

A) 80%

B) 70%

C) 75%

D) 62%

E) 65%

**8. The amount of water (in ml) that should be added to reduce 9 ml lotion, containing 50% alcohol, to a lotion containing 30% alcohol is ?**

A) 6ml

B) 11 ml

C) 15ml

D) 9ml

E) 7ml

**9. If a man buys 1 lt of milk for Rs.12 and mixes it with 20% water and sells it for Rs.15, then what is the percentage of gain ?**

A) 25%

B) 30%

C) 17%

D) 19%

E) 23%

**10. One type of liquid contains 25 % of benzene, the other contains 30% of benzene. A can is filled with 6 parts of the first liquid and 4 parts of the second liquid. Find the percentage of benzene in the new mixture.**

A) 27%

B) 26%

C) 29%

D) 21%

E) 19%

**Solutions:**

**1. B)**Let the capacity of the pot be 'P' litres.

Quantity
of milk in the mixture before adding milk = 4/9 (P - 4)

After
adding milk, quantity of milk in the mixture = 6/11 P.

6P/11
- 4 = 4/9(P - 4)

10P
= 396 - 176 => P = 22.

The
capacity of the pot is 22 liters.

**2. D)**Milk = 3/5 x 20 = 12 liters, water = 8 liters

If
10 liters of mixture are removed, amount of milk removed = 6 liters and amount
of water removed = 4 liters.

Remaining
milk = 12 - 6 = 6 liters

Remaining
water = 8 - 4 = 4 liters

10
liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.

The
ratio of milk and water in the new mixture = 16:4 = 4:1

If
the process is repeated one more time and 10 liters of the mixture are removed,

then
amount of milk removed = 4/5 x 10 = 8 liters.

Amount
of water removed = 2 liters.

Remaining
milk = (16 - 8) = 8 liters.

Remaining
water = (4 -2) = 2 liters.

Now
10 lts milk is added => total milk = 18 lts

The
required ratio of milk and water in the final mixture obtained

=
(8 + 10):2 = 18:2 = 9:1.

**3. A)**Quantity of fruit juice in the mixture = 90/100 (70) = 63 litres.

After
adding water, juice would form 87 1/2% of the mixture.

Hence,
if quantity of mixture after adding x liters of water, (87 1/2) / 100 x = 63
=> x = 72

Hence
72 - 70 = 2 litres of water must be added.

**4. B)**Number of liters of water in 150 liters of the mixture = 20% of 150 = 20/100 x 150 = 30 liters.

P
liters of water added to the mixture to make water 25% of the new mixture.

Total
amount of water becomes (30 + P) and total volume of mixture is (150 + P).

(30
+ P) = 25/100 x (150 + P)

120
+ 4P = 150 + P => P = 10 liters.

**5. B)**Here total parts of milk and water in the solution is 6+2 = 8 parts

1part
= 640/8 = 80

old
mixture contains 6parts of milk and 2 parts of water(6:2).

To
get new mixture containing half milk and half water, add 4parts of water to the
old mixture then 6:(2+4) to make the ratio same.

i.e,
4 x 80 = 320 ml.

**6. A)**Given the three mixtures ratio as (1:2),(2:3),(3:4)

(1+2),(2+3),(3+4)

Total
content = 3,5,7

Given
equal quantities of the three mixtures are mixed, then LCM of 3, 5, 7 = 105

105/3
= 35 , 105/5 = 21 , 105/7 = 15

Now,
the individual equal quantity ratios are (35x1, 35x2), (21x2, 21x3), (15x3,
15x4)

(35,70),
(42,63), (45,60)

So
overall mixture ratio of milk and water is

35+42+45
: 70+63+60

122:193

But
in the question asked the ratio of water to milk = 193 : 122

**7. A)**Water in 60 gm mixture=60 x 75/100 = 45 gm. and Milk = 15 gm.

After
adding 15 gm. of water in mixture, total water = 45 + 15 = 60 gm and

weight
of a mixture = 60 + 15 = 75 gm.

So
% of water = 100 x 60/75 = 80%.

**8. A)**Let us assume that the lotion has 50% alcohol and 50% water.

ratio
= 1:1

As
the total solution is 9ml

alcohol
= water = 4.5ml

Now
if we want the quantity of alcohol = 30%

The
quantity of water = 70%

The
new ratio = 3:7

Let
x ml of water be added

We
get, (4.5)/(4.5 + x) = 3/7 => x = (4 × 4.5)/3 => x = 4 × 1.5 => x = 6

Hence
6ml of water is added

**9. A)**He has gain = 15 - 12 = 3,

Gain%
= (3/12) x 100 = (100/4) = 25.

He
has 25% gain.

**10. A)**Let the percentage of benzene = X

(30
- X)/(X- 25) = 6/4 = 3/2

=>
5X = 135

X
= 27

So,
required percentage of benzene = 27 %