# Mixture and Alligation : Set 2 for SBI PO

Q.1) A mixture of 70 litres of milk and water contains 20% water. How many litres of water is to be added so that the water may be 30% of the mixture?

a) 70 litres

b) 10 litres

c) 30 litres

d) 20 litres

e) 40 litres

b

Original mixture contains 20% water and 80% milk. Now water is to be added (0% milk) to make it 30% water (70% milk)

For 7 litre of milk and water one litre of water is to be added. So for 70 litres of milk and water 10 litres (70×1/7) is to be added.

Q.2) From a cask of wine containing 100 litres, 10 litres are drawn out and the cask is filled up with water. If the process is repeated once more, how many litres of wine will be left in the cask?

a) 100 litres

b) 91 litres

c) 80 litres

d) 81 litres

e) 70 litres

d

Wine left in the cask after 2nd operation =100(1-10/100)2=100×9/10×9/10=81 litres.

Q.3) Two alloys of silver and copper contains silver and copper in the ratio 4:1 and 5:4. What quantities of each should be mixed to prepare silver being 70% of the mixture.

a) 13:9

b) 9:13

c) 7:3

d) 3:7

e) 1:1

a

1st mixture, Silver to copper 4:1 or  4/5  :1/5

2nd mixture, Silver to copper 5:4 or  5/9  :4/9

Required mixture, silver to copper 70% or 70:30  7/10  :3/10

It should be in the ratio 13:9.

Q.4) Two vessels contain milk and water in the ratio 3:2 and 7:2 respectively. In what ratio these are to be mixed to prepare a 3rd mixture containing milk and water in the ratio 2:1?

a) 3:5

b) 5:3

c) 3:2

d) 5:2

e) 2:1

b

1st mixture, milk to water 3:2 or  3/5  :  2/5

2nd mixture, milk to water 7:2 or  7/9  :2/9

3rd mixture, milk to water 2:1 or  2/3  :1/3

By allegation method:

It should be mixed in the ratio 5:3.

Q.5) Equal amounts of water were poured into two empty jars of different capacities, which made on jars  full and the other jar  full. If the water in the jar with lesser capacity is then poured into the Jar with greater capacity, then the part of the larger jar filled with water is,

a) 1/4

b) 3/4

c) 2/3

d) 1/12

e) None of these

e

Amounts of water in two jars are equal ; the jar with the greater capacity is  1/4  full, and the Jar with lesser capacity is  1/3  full

When the water in smaller jar is poured into the larger jar, the addition of an equal amount of water will double the amount in the larger jar, which will then be

2×1/4=1/2

Q.6) When processing flower nectar into honey, a considerable amount of water is added. How much flower nectar must be processed to yield 1kg of honey, if nectar contains 70% water and the honey obtained from this nectar contains 17% water?

a) 4.11kg

b) 1.76kg

c) 0.36kg

d) 2.77kg

e) None of these

d

Given that nectar contains 70% water.

And honey obtained contains 17% water

It means that out of 1 kg honey 17% is water

i.e. pure honey = 0.83 kg

which is 30% of the flower nectar

70% of water

Now, let quantity of flower

Nectar processed be x kg

Then, 0.3 x = 0.83

X= 0.83/0.3 = 2.77kg

Q.7) Three vessels containing mixtures of milk and water are of capacities which are in the ratio 2:3:4. The ratio of milk and water in the three vessels are 3:2, 4:1 and 3:2 respectively. If one fourth the contents of the first vessel, one- third of that of the second vessel and half of that of the third vessel are mixed, what is the ratio of milk and water in the new mixture?

a) 17 : 23

b) 23: 12

c) 15: 29

d) 1: 2

e) None of these

b

Part of milk in the resultant solution

=1/4×2/9×3/5+1/3×3/9×4/5+1/2×4/9×3/5=23/90

Part of water in the resultant  solution,

=1/4×2/9×2/5+1/3×3/9×1/5+1/2×4/9×2/5=2/15

Required ratio =23/90  :2/15=23 :12

Q.8)  400gm of salt solution has 60% salt in it. How much salt should be added to make it 40% in the solution?

a) 60gm

b) 80gm

c) 100gm

d) 120gm

e) None of these

c

3 : 1

Since, 4 = 400gm; 1=100gm

Q.9)  A container contained 160 litres. From this container 16 litre of Juice was taken out and replaced by water. This process was further repeated two times. How much Juice is now contained in the container?

a) 116.64 litre

b) 154.26 litre

c) 144.23 litre

d) 128.32 litre

e) None of these

a

Remaining quantity = (x(1-y/x)n

= (160 (1-16/160)3= 116.64 litres

Q.10)  Vessels A and B contain mixture of milk and water in the ratio 1:4 and 3:2 respectively. In what ratio should quantities of mixture be taken from A and B to form a mixture in which milk to water is in the ratio 2:3?

a) 1 : 5

b) 1 : 1

c) 2 : 1

d) 2 : 3

e) None of these