Quiz: Mixture and Alligation Set 3

1. The average weekly salary per head of the entire staff of a factory consisting ofsupervisors and the labourers is Rs. 55. The average salary per head of the supervisors is Rs. 300 and that of the labourers is Rs. 40. Given that the number of supervisors is 10, find the number of labourers in the factory.
A.160
B.120
C.155
D.143
E.None of these

Solution:
40…………………………………..300
………………….55…………………….
245…………………………………15
(Number of labourers)/(Number of supervisors) = 245/15 = 16.33/1 = 16/1
16:1 = 160:10
2. A man travelled a distance of 40 km. in 5 hours partly on foot at the rate of 7 km per hour and partly on bicycle at 12 km. per hour. Find the distance travelled on foot ?
A.36km
B.24km
C.32km
D.28km
E.None of these

Solution:
7……………………………………….12
…………………..40/5=8………………..
4………………………………………..1
Time taken on foot /Time taken on bicycle = 4:1
Distance travelled on foot = 4*7 = 28km
3. Milk contains 15% water. What quantity of pure milk should be added to 50 litres of milk to reduce the quantity of water to 12% ?
A.16litres
B.14litres
C.12.5litres
D.17litres
E.None of these

Solution:
Ans: 50*15/100 = (50+x)*12/100
7.5 *100 = 600+12x
12x = 150
X = 150/12 = 12.5litre
4. Dhal worth Rs. 110 per kg and Rs. 95 per kg are mixed with a third variety in the ratio 1:1:2. If the mixture is worth Rs. 115 per kg, the price of the third variety per kg will be
A.Rs.127.5
B.Rs.115.75
C.Rs.125
D.Rs.117.5
E.None of these

Solution:
1st two type of Dhal = 110+95/2 = 102.5
102.5…………………………………..X
……………..115……………………….
x-115……………………………………12.5
x-115 = 12.5
x = 127.5
5. A zookeeper counted the heads of the animals in a zoo and found it to be 100. When he counted the legs of the animals he found it to be 340. If the zoo had either pigeons or elephants, how many pigeons were there in the zoo?
A.45
B.30
C.70
D.50
E.None of these

Solution:
total number of legs = 4x + 2(100-x) = 340
4x + 200 – 2x = 340
2x = 140
x = 70
P = 100-70 =30
6. In a 70 litres mixture of milk and water, % of water is 30%. The milkman gave 20 litres of this mixture to a customer and then added 20 litres of water to the remaining mixture. What is the % of milk in the final mixture ?
A.48%
B.50%
C.40%
D.53%
E.None of these

Solution:
20litre given remaining = 70-20 = 50litre
Quantity of milk = 50*70/100 = 35litre
Quantity of water = 50-35 = 15litre
20litres of water added = 50+20 = 70
% of milk = 35*100/70 =50%
7. A company is creating a new signature drink. They are using two alcoholic ingredients in the drink vodka and gin. They are using two non-alcoholic ingredients in the drink: orange juice and cranberry juice. The alcoholic ingredients contain 50% alcohol. The non-alcoholic ingredients contain no alcohol. How many litres of non-alcoholic ingredients must be added to 5 litres of alcoholic ingredients to produce a mixture that is 20% alcohol?
A.8
B.6.5
C.7.5
D.9
E.None of these

Solution:
(5+x) (20%) = 5(50%) + x(0%)
(5+x) 0.2 = 5(0.5) + 0
1+0.2x = 2.5
X = 2.5-1/0.2 = 1.5/0.2 = 7.5
8. A can contains 30liter of juice, from this container 5litres of juice was taken out and replaced by water. This process was repeated further two times. How much juice is now contained by the container?
A.21
B.13
C.15
D.17
E.None of these

Solution:
Quantity of milk in the final mixture = 30[1-(5/30)]3
= 30*(5/6) 3
= 30*125/216 = 17.36 liter = 17
9. Rani mixes 70kg of sugar worth Rs.28.50 per kg with 100kg of sugar worth Rs.30.50 per kg. At what rate shall he sell the mixture to gain 10% ?
A.Rs.32.64
B.Rs.31.50
C.Rs.30.46
D.Rs.29.75
E.None of these

Solution:
70/100 = 100x – 30.50(110)/28.50(110)-100x
0.7 = 100x-3355/3135-100x
2194.5 – 70x =  100x-3355
170x = 5549.5
X = 32.64
10. 90 litres of a mixture of milk and water contains 20% water. How much water should be added so that the mixture has 28% water ?
A.18litres
B.12litres
C.10litres
D.8litres
E.None of these