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 %
