## Allegations and Mixtures Practice Set – 2

Allegations and Mixtures Practice Set – 2
1. In a mixture of milk and water, the proportion of water by weight was 75%. If in the 60 gms mixture 15 gms water was added, what would be the percentage of water in the new mixture?
a) 75%
b) 88%
c) 90%
d) 100%
e) None of these
Explanation:
In 60 gm of mixture, Quantity of water = 60 × 75/100 = 45gm
Quantity of milk = 15 gm
After mixing 15 gm of more water, Quantity
of water in the new mixture = 45 + 15 = 60 gm
Quantity of water in 75 gm of mixture = 60 gm
100 gm of mixture will contain = 60/75 × 100 = 80% of water

2. A man purchased 35 kg of rice at the rate of Rs. 9.50 per kg and 30 kg at the rate of Rs. 10.50 per kg. He mixed the two. Approximately, at what price (in Rupees) per kg should he sell the mixture to make 35 per cent profit in the transaction?
a) 12
b) 12.50
c) 13
d) 13.50
e) 13.25
Explanation:
CP of 65 kg of the mixture = Rs. (35 × 9.50 + 30 × 10.50)
= Rs. (332.5 + 315) = Rs. 647.5
Rate per kg of the mixture = Rs 647.5/65
Required rate = 647.5/65 135/100 = Rs 13.50/kg

3. In 1 kg mixture of sand and iron, 20% is iron. How much sand should be added, so that the proportion of iron becomes 5%?
a) 3 kg
b) 4 gms
c) 5 gms
d) 6 kg
e) None of these
Explanation:
Amount of iron in 1 kg mixture = 20% of 1000 gms
= (20 × 1000) / 100 gms = 200 gms
Amount of sand in mixture = (1000 - 200) gms = 800 gms
Now, let the total mixture is x kg in which iron is 20%
According to the question, 5% of x = 200 gm
5% of x = 200 gm
= (5 × x) / 100 = 200
x = (200 × 100) / 5 gms
x = 20000/5 = 4000 gms
Required answer = 4000 gms - 1000 gms = 3000 gms = 3 kg

4. The wheat sold by a grocer contained 10% low quality wheat. What quantity of good quality wheat should be added to 150 kgs of wheat so that the percentage of low quality wheat becomes 5%?
a) 150 kgs
b) 135 kgs
c) 50 kgs
d) 85 kgs
e) None of these
Explanation:
Good quality content in 150 kgs of wheat = 90% of 150 = 135 kg.
In new mixture, low quality wheat is 5%, so good quality wheat 95%
5% of the new mixture = 15 kg,
New mixture = (15 × 100) / 5 = 300 kg
Good quality of wheat added = (300 - 150) kg. = 150 kg

5. When one litre of water is added to a mixture of acid and water, the new mixture contains 20% acid. When one litre of acid is added to the new mixture, then the resulting mixture contains 100/3 % acid. The percentage of acid in the original mixture was
a) 20%
b) 22%
c) 24%
d) 25%
e) 23%
Explanation:
If there be 1 litre of acid in 4 litres of mixture,
then in case I. Percentage of acid =1 / (4 + 1) × 100 = 20%
Case II, Percentage of acid = 2/6 × 100 = 100/3 %
Percentage of acid in original mixture = 25%

6. A grocer purchased 2 kg. of rice at the rate of Rs. 15 per kg. and 3 kg. of rice at the rate of Rs. 13 per kg. At what price per kg should he sell the mixture to earn 100/3 % profit on the cost price?
a) Rs. 28.00
b) Rs. 20.00
c) Rs. 18.40
d) Rs. 17.40
e) None of these
Explanation:
Mixture : 2 kg of rice at Rs.
15/kg + 3 kg of rice at Rs. 13/kg
Total weight = 2 + 3 = 5 kg
Total cost price = (2 × 15) + (3 × 13) = 30 + 39 = Rs. 69
Cost price per kg of the mixture = 69/5 = Rs 13.80
Selling price to get 100/3 % profit
= (10 + 100/3)/100 × Rs 13.80 = Rs 18.40

7. Two barrels contain a mixture of ethanol and gasoline. The content of the ethanol is 60% in the first barrel and 30% in the second barrel. In what ratio must the mixtures from the first and the second barrels be taken to form a mixture containing 50% ethanol?
a) 1 : 2
b) 2 : 1
c) 2 : 3
d) 3 : 2
e) None of these

8. A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?
a) 5 litres, 7 litres
b) 7 litres, 4 litres
c) 6 litres, 6 litres
d) 6 litres, 5 litres
e) 4 litres, 8 litres

9. A and B are two alloys of gold and copper prepared by mixing metals in the ratio 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) 5 : 7
b) 5 : 9
c) 7 : 5
d) 9 : 5
e) None of these
Explanation:
In 1 kg of alloy A,
Gold = 7/18
Copper = 2/9
In 1 kg of alloy B,
Gold = 7/18 Copper = 11/18
Ratio of gold and copper in Alloy C = 7/9 + 7/18 : 2/9 + 11/18 = 21 : 15 = 7 : 5

10. A container has 30 litres of water. If 3 litres of water is replaced by 3 litres of spirit and this operation is repeated twice, what will be the quantity of water in the new mixture?
a) 24 litres
b) 23 litres
c) 24.3 litres
d) 23.3 litres
e) None of these