Mixture and Alligations Questions for IBPS PO Prelims

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Mixture and Alligations Questions for IBPS RRB and PO Prelims

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Question 1: In a mixture, the quantity of water is 20% less than the quantity of juice. When 90 liters of mixture is taken out and 70 liters of water is added into it, then the quantity of juice will be 11.11% more than the quantity of water. Find out the initial quantity of water in the mixture.

a) 750 liters

b) 600 liters

c) 500 liters

d) 800 liters

e) 450 liters

1) Answer (B)

Solution:

In a mixture, the quantity of water is 20% less than the quantity of juice.
Let’s assume the initial quantity of juice is 5y.
Initial quantity of water = 5y of (100-20)%
= 5y of 80%
= 4y
When 90 litres of mixture is taken out and 70 liters of water is added into it, then the quantity of juice will be 11.11% more than the quantity of water.
$\frac{5y-50}{4y-40+70} = \frac{10}{9}$
$\frac{5y-50}{4y+30} = \frac{10}{9}$
$\frac{y-10}{4y+30} = \frac{2}{9}$
9y-90 = 8y+60
9y-8y = 60+90
y = 150
Initial quantity of water in the mixture = 4y
= $4\times150$
= 600 liters
Hence, option b is the correct answer.

Question 2: A tank contains 120 litres of milk and 80 litres of water. If __ litres of mixture is taken out from the tank and __ litres of milk is added to the tank then the final quantity of milk is 57.14% more than the final quantity of water.
Which of the following values can fill in the blanks appropriately?
(i) 60, 4
(ii) 95, 3
(iii) 140, 2

a) Only (ii) and (iii)

b) Only (i) and (ii)

c) All (i), (ii) and (iii)

d) Only (iii)

e) Only (i) and (iii)

2) Answer (B)

Solution:

The final quantity of milk is 57.14% more than the final quantity of water.
Final quantity of milk = Final quantity of water + $\frac{4}{7}\times$Final quantity of water
Final quantity of milk = $\frac{11}{7}\times$Final quantity of water
Ratio of the final quantity of milk and water is 11:7 respectively.

(i) 60, 4
60 litres of mixture is taken and 4 litres of milk is added from the tank.
Ratio of initial quantity of milk and water = 120 : 80
= 3 : 2
Final quantity of milk = 120 – $\frac{3}{3+2}\times$60 + 4 = 88 litres
Final quantity of water = 80 – $\frac{2}{3+2}\times$60 = 56
Ratio of final quantity of milk and water = 88 : 56
= 11:7
Given values satisfy the conditions of the question.

(ii) 95, 3
95 litres of mixture is taken and 3 litres of milk is added from the tank.
Ratio of initial quantity of milk and water = 120 : 80
= 3 : 2
Final quantity of milk = 120 – $\frac{3}{3+2}\times$95 + 3 = 66 litres
Final quantity of water = 80 – $\frac{2}{3+2}\times$95 = 42
Ratio of final quantity of milk and water = 66 : 42
= 11:7
Given values satisfy the conditions of the question.

(iii) 140, 2
140 litres of mixture is taken and 2 litres of milk is added from the tank.
Ratio of initial quantity of milk and water = 120 : 80
= 3 : 2
Final quantity of milk = 120 – $\frac{3}{3+2}\times$140 + 2 = 38 litres
Final quantity of water = 80 – $\frac{2}{3+2}\times$140 = 24
Ratio of final quantity of milk and water = 38 : 24
= 19:12
Given values do not satisfy the conditions of the question.
Hence, the correct answer is Option B

Question 3: There are two tanks A and B which contain a mixture of milk and water. Tank A contains milk and water in the ratio of 4 : 1 and tank B contains milk and water in the ratio of 3 : 1. The total quantity of mixture is 60 litres when $\frac{1}{5}$ of mixture from tank A and $\frac{1}{4}$ of mixture from tank B are mixed. The initial quantity of milk in tank A is 40 litres more than the initial quantity of water in tank B. What is the initial quantity of water in tank A?

a) 20 litres

b) 24 litres

c) 16 litres

d) 12 litres

e) None of the above

3) Answer (A)

Solution:

Ratio of milk and water in tank A is 4 : 1
Let the quantity of milk and water in tank A is 4p and p respectively.
Ratio of milk and water in tank B is 3 : 1
Let the quantity of milk and water in tank B is 3q and q respectively.
The total quantity of mixture is 60 litres when $\frac{1}{5}$ of mixture from tank A and $\frac{1}{4}$ of mixture from tank B are mixed.
$\Rightarrow$ $\frac{1}{5}$(4p+p) + $\frac{1}{4}$(3q+q) = 60
$\Rightarrow$ p + q = 60……….(1)
The quantity of milk in tank A is 40 litres more than quantity of water in tank B.
$\Rightarrow$ 4p = q + 40…….(2)
Adding (1) and (2),
5p + q = q + 100
p = 20
$\therefore$ Initial quantity of water in tank A = p = 20 litres
Hence, the correct answer is Option A

Question 4: In a 50 litres mixture of milk and water, percentage of water is 20%. The milkman sold 10 litres of this mixture and added 32 litres of milk and 24 litres of water in the remaining mixture. What is the percentage of water in the new mixture?

a) 33$\frac{1}{3}$%

b) 31$\frac{1}{3}$%

c) 31$\frac{2}{3}$%

d) 33$\frac{2}{3}$%

e) None of the above

4) Answer (A)

Solution:

Total initial mixture = 50 litres
Milkman sold 10 litres of this mixture
Remaining mixture = 40 litres
Percentage of water = 20%
Quantity of water in the remaining mixture = $\dfrac{20}{100}\times$40 = 8 litres
Quantity of milk in the remaining mixture = 40 – 8 = 32 litres
After adding 32 litres of milk and 24 litres of water in the remaining mixture,
Quantity of milk in the new mixture = 32 + 32 = 64 litres
Quantity of water in the new mixture = 8 + 24 = 32 litres
$\therefore$ Percentage of water in the new mixture = $\dfrac{32}{64+32}\times$100
= $\dfrac{32}{96}\times$100
= 33$\frac{1}{3}$%
Hence, the correct answer is Option A

Question 5: In a mixture of 280 litres, the quantity of water is 25% less than the quantity of juice. If 20 litres and ‘y’ litres of juice and water are added into the initial mixture, then the quantity of juice and water in the new mixture will be 9:8 respectively. Find out the value of ‘y’.

a) 25

b) 40

c) 50

d) 35

e) None of the above

5) Answer (B)

Solution:

In a mixture of 280 litres, the quantity of water is 25% less than the quantity of juice.
quantity of water = 75% of quantity of juice
quantity of juice : quantity of water ⇒ 4:3
quantity of juice = 280 of (4/7) = 160 litres
quantity of water = 280 of (3/7) = 120 litres
If 20 litres and ‘y’ litres of juice and water are added into the initial mixture, then the quantity of juice and water in the new mixture will be 9:8 respectively.
$\frac{160+20}{120+y} = \frac{9}{8}$

$\frac{180}{120+y} = \frac{9}{8}$

$\frac{20}{120+y} = \frac{1}{8}$

160 = 120+y
y = 160-120 = 40
Hence, option b is the correct answer.

Question 6: A tank contains a mixture of milk and water in the ratio of 9 : 7 respectively. 32 litres of mixture is taken out and the tank is filled with 90 litres of milk, the ratio between milk and water becomes 2 : 1 respectively. What is the initial quantity of water in the tank?

a) 210 litres

b) 180 litres

c) 280 litres

d) 140 litres

e) 150 litres

6) Answer (D)

Solution:

Initial ratio of milk and water = 9 : 7

Let the initial quantity of milk and water is 9p and 7p

32 litres of mixture is taken out. The quantity of milk and water taken out will be in the same ratio 9 : 7.

Quantity of milk taken out = $\frac{9}{9+7}\times32$ = 18 litres

Remaining quantity of milk = 9p – 18

Quantity of water taken out = $\frac{7}{9+7}\times32$ = 14 litres

Remaining quantity of water = 7p – 14

According to the problem,

$\frac{9p-18+90}{7p-14}=\frac{2}{1}$

$9p+72=14p-28$

$5p=100$

$p=20$

$\therefore$ Initial quantity of water = 7p = 7 x 20 = 140

Hence, the correct answer is Option D

Question 7: In a mixture, the initial quantity of milk and water is 4:1 respectively. If ‘y’ and (y-15) litres of milk and water are poured into the mixture respectively, then in the mixture the new ratio of milk and water will be 7:2 respectively. If 40 litres of mixture is taken out from the initial mixture and (y-3) and (y-7) litres of milk and water are poured into the mixture respectively, then in the mixture, the new ratio of milk and water will be 49:15 respectively. Find out the value of ‘y’.

a) 50

b) 45

c) 30

d) 40

e) Cannot be determined

7) Answer (B)

Solution:

In a mixture, the initial quantity of milk and water is 4:1 respectively.
Let’s assume the initial quantity of milk and water in the mixture is 4z and z respectively.
If ‘y’ and (y-15) litres of milk and water are poured into the mixture respectively, then in the mixture the new ratio of milk and water will be 7:2 respectively.
$\frac{4z+y}{z+(y-15)} = \frac{7}{2}$
8z+2y = 7z+7y-105
z-5y = -105
5y-z = 105
z = 5y-105 Eq.(i)
If 40 litres of mixture is taken out from the initial mixture and (y-3) and (y-7) itres of milk and water are poured into the mixture respectively, then in the mixture the new ratio of milk and water will be 49:15 respectively.
$\frac{4z-32+(y-3)}{z-8+(y-7)} = \frac{49}{15}$

$\frac{4z-35+y}{z-15+y} = \frac{49}{15}$
60z-525+15y = 49z-735+49y
11z-34y = -735+525
34y-11z = 210 Eq.(ii)
Put Eq.(i) in Eq.(ii).
34y-11(5y-105) = 210
34y-55y+1155 = 210
21y = 945
y = 45
Hence, option b is the correct answer.

Question 8: In 2024 litres of the mixture, the ratio between the quantity of milk and water is 5:3 respectively. If (y+44) litres of milk and ‘y’ litres of water is poured into the mixture, then the ratio between the quantity of milk and water will be 27:16 respectively. Find out the value of (y+8).

a) 49

b) 41

c) 45

d) 47

e) None of the above

8) Answer (A)

Solution:

In 2024 litres of the mixture, the ratio between the quantity of milk and water is 5:3 respectively.
Initial quantity of milk = $\frac{5}{8}\times2024$
= 1265
Initial quantity of water = $\frac{3}{8}\times2024$
= 759
If (y+44) litres of milk and ‘y’ litres of water is poured into the mixture, then the ratio between the quantity of milk and water will be 27:16 respectively.

$\frac{1265+(y+44)}{759+y} = \frac{27}{16}$

$\frac{1309+y}{759+y} = \frac{27}{16}$

20944+16y = 20493+27y
27y-16y = 20944-20493
11y = 451
y = 41
value of (y+8) = 41+8 = 49
Hence, option a is the correct answer.

Question 9: In a jar P, (y-35) litres of mixture is available, where the quantity of water is 63.63% less than the quantity of juice. In another jar Q, ‘y’ litres of mixture is available, where the quantity of juice is $\frac{3}{7}$ times more than the quantity of water. If the mixture of both the jars is mixed together, then the quantity of water will be 452 litres. Find out the value of ‘y’.

a) 520

b) 560

c) 640

d) 680

e) None of the above

9) Answer (D)

Solution:

In a jar P, (y-35) litres of mixture is available, where the quantity of water is 63.63% less than the quantity of juice.
In a jar P, the ratio between the quantities of juice and water is 11:4 respectively.
In another jar Q, ‘y’ litres of mixture is available, where the quantity of juice is $\frac{3}{7}$ times more than the quantity of water.
In a jar Q, the ratio between the quantities of juice and water is 10:7 respectively.
If the mixture of both the jars is mixed together, then the quantity of water will be 452 litres.
(4/15) of (y-35) + (7/17) of y = 452

68y-2380+105y = 115260
173y = 115260+2380 = 117640
y = 680
Hence, option d is the correct answer.

Question 10: In a mixture, the ratio between the quantities of milk and water is 5:7 respectively. If 22 litres of water is poured into the mixture, then the ratio between the quantities of milk and water will be 2:3 respectively. Find out the initial quantity of mixture.

a) 652 litres

b) 504 litres

c) 528 litres

d) 616 litres

e) None of the above

10) Answer (C)

Solution:

In a mixture, the ratio between the quantities of milk and water is 5:7 respectively.
Let’s assume the ratio between the quantities of milk and water is 5y and 7y respectively.
If 22 litres of water is poured into the mixture, then the ratio between the quantities of milk and water will be 2:3 respectively.
$\frac{5y}{7y+22} = \frac{2}{3}$

15y = 14y+44
y = 44
Initial quantity of mixture = 5y+7y = 12y = $12\times44$
= 528 litres
Hence, option c is the correct answer.

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Question 11: In a ‘y’ liters of mixture, the quantity of milk is 37.5% more than the quantity of water. If 10 litres of water is added into the mixture, then the ratio between the quantity of milk to water will become 4:3. Find out the difference between the quantity of milk and water in the initial mixture.

a) 125 liters

b) 175 liters

c) 180 liters

d) 120 liters

e) None of the above

11) Answer (D)

Solution:

In a ‘y’ liters of mixture, the quantity of milk is 37.5% more than the quantity of water.
The ratio between the initial quantity of milk and water is 11:8 respectively.
If 10 litres of water is added into the mixture, then the ratio between the quantity of milk to water will become 4:3.
$\frac{\frac{11}{19}y}{\frac{8}{19}y + 10} = \frac{4}{3}$

$\frac{11y}{8y + 190} = \frac{4}{3}$

33y = 32y + 760
y = 760
Difference between the quantity of milk and water in the initial mixture = $\frac{11}{19}y – \frac{8}{19}y$
= $\frac{3}{19}y$

= $\frac{3}{19}\times760$

= 120 liters
Hence, option d is the correct answer.

Question 12: In a ‘y’ litres of mixture, the ratio between the quantities of milk and water is 11:7 respectively. If 17 litres and 49 litres of milk and water is poured into the mixture, then the ratio between the quantities of milk and water will be 7:5 respectively. Find out the value of ‘y’.

a) 792

b) 774

c) 756

d) 738

e) None of the above

12) Answer (B)

Solution:

$\frac{\frac{11}{18}y + 17}{\frac{7}{18}y + 49} = \frac{7}{5}$

$\frac{11y + 306}{7y + 882} = \frac{7}{5}$

55y + 1530 = 49y + 6174
55y – 49y = 6174-1530
6y = 4644
y = 774
Hence, option b is the correct answer.

Question 13: There are two drums A and B having (y-75) litres and ‘y’ litres of mixture respectively. The quantity of juice in drum A is 12.5% less than the quantity of water in the same drum. In drum B, the ratio between the quantity of juice and water is 11:7 respectively. If the difference between the quantity of water in both the drums is 64 litres, then find out the quality of juice in drum A.

a) 316 litres

b) 256 litres

c) 331 litres

d) 301 litres

e) None of the above

13) Answer (D)

Solution:

The quantity of juice in drum A is 12.5% less than the quantity of water in the same drum.
The quantity of juice in drum A = ⅞ of the quantity of water in the same drum
So in drum A, the ratio between the quantity of juice and water is 7:8 respectively.
If the difference between the quantity of water in both the drums is 64 litres.
(y-75) of (8/15) – y of (7/18) = 64
$\frac{8y}{15} – 40 – \frac{7y}{18} = 64$

$\frac{8y}{15} – \frac{7y}{18} = 64+40 = 104$

$\frac{48y}{90} – \frac{35y}{90} = 104$

$\frac{13y}{90} = 104$

y = 720 litres
Total quantity of mixture in drum A = (y-75) = 720-75 = 645 litres
Quality of juice in drum A = 645 of (7/15)
= 301 litres
Hence, option d is the correct answer.

Question 14: In a mixture of milk and water, the quantity of water is $\frac{4}{35}$ times less than the quantity of milk. If ‘y’ litres of milk and (y+10) litres of water is poured into the mixture, then the quantity of milk will be 11.11% more than the quantity of water. If the initial quantity of water is 775 litres, then find out the value of ‘y’.

a) 15

b) 25

c) 10

d) 20

e) None of the above

14) Answer (B)

Solution:

In a mixture of milk and water, the quantity of water is $\frac{4}{35}$ times less than the quantity of milk.
If the initial quantity of water is 775 litres.
Initial quantity of milk = $\frac{35}{31}\times 775$ = 875 litres.
If ‘y’ litres of milk and (y+10) litres of water is poured into the mixture, then the quantity of milk will be 11.11% more than the quantity of water.
$\frac{875 + y}{775 + (y+10)} = \frac{10}{9}$

$\frac{875 + y}{785 + y} = \frac{10}{9}$

7875 + 9y = 7850 + 10y
y = 7875-7850 = 25
Hence, option b is the correct answer.

Question 15: In a drum P, ‘z’ litres of mixture is available where the quantity of juice and water is 3:5 respectively. In another drum Q, (z-240) litres of mixture is available where the quantity of juice and water is 7:4 respectively. If the total quantity of juice from both the drums together is 980 litres, then find out the value of ‘z’.

a) 1250

b) 1040

c) 1160

d) 1080

e) 1120

15) Answer (E)

Solution:

$\frac{3}{8} \times z+ \frac{7}{11} \times (z-240) = 980$

$\frac{3z}{8} + \frac{7z}{11} – \frac{1680}{11} = 980$

$\frac{33z}{88} + \frac{56z}{88} = 980 + \frac{1680}{11}$

$\frac{89z}{88} = \frac{1680 + 10780}{11}$

$\frac{89z}{88} = \frac{12460}{11}$

$\frac{89z}{8} = \frac{12460}{1}$

$z = 140\times8 = 1120$
Hence, option e is the correct answer.

Question 16: In 820 litres of a mixture, the ratio between the quantities of milk and water is 4:1 respectively. If 40 litres of mixture is taken out and some quantity of water is added into the mixture, then the ratio between the quantities of milk and water will be 3:1 respectively. Find out the quantity of water which was added in the mixture.

a) 50 litres

b) 56 litres

c) 44 litres

d) 48 litres

e) 52 litres

16) Answer (E)

Solution:

In a 820 litres of mixture, the ratio between the quantities of milk and water is 4:1 respectively.
Initial quantity of milk = $\frac{4}{5}\times820$
= 656
Initial quantity of water = $\frac{1}{5}\times820$
= 164
If 40 liters of mixture is taken out and some quantity of water is added into the mixture, then the ratio between the quantities of milk and water will be 3:1 respectively.
Let’s assume the quantity of water is added into the mixture is y.
$\frac{656-32}{164+y-8} = \frac{3}{1}$

$\frac{624}{156+y} = \frac{3}{1}$

156+y = 208
y = 208-156 = 52 litres
Hence, option e is the correct answer.

Question 17: In a bucket P, 847 litres of mixture is available, where the ratio between the quantities of juice and water is 5:2 respectively. Another bucket Q is having 195 litres of juice and the remaining quantity is water. If the mixture of both buckets is poured into a big bucket R, then the total quantity of water in this bucket will be 31.25% of the total quantity of juice in this bucket. Find out the initial quantity of water in the bucket Q.

a) 24 litres

b) 6 litres

c) 18 litres

d) 12 litres

e) 8 litres

17) Answer (E)

Solution:

In a bucket P, 847 litres of mixture is available, where the ratio between the quantities of juice and water is 5:2 respectively.
Quantity of juice in bucket P = $\frac{5}{7}\times847$ = 605 litres
Quantity of water in bucket P = $\frac{2}{7}\times847$ = 242 litres
Another bucket Q is having 195 litres of juice and the remaining quantity is water.
Quantity of juice in bucket Q = 195 litres
Let’s assume the quantity of water in bucket Q is y.
If the mixture of both buckets is poured into a big bucket R, then the total quantity of water in this bucket will be 31.25% of the total quantity of juice in this bucket.
$\frac{605+195}{242+y} = \frac{16}{5}$

$\frac{800}{242+y} = \frac{16}{5}$

$\frac{50}{242+y} = \frac{1}{5}$

250 = 242+y
Initial quantity of water in the bucket Q = y = 250-242 = 8 litres
Hence, option e is the correct answer.

Question 18: In a 765 litres of mixture, the quantity of milk is 20% less than the quantity of water. If ‘y’ litres of milk is poured into the mixture, the ratio between quantity of milk and water will be 16:17 respectively, then find out the value ‘y’.

a) 45

b) 60

c) 90

d) 75

e) None of the above

18) Answer (B)

Solution:

In a 765 litres of mixture, the quantity of milk is 20% less than the quantity of water.
So the ratio of the initial quantity of milk and water will be 4:5 respectively.
Initial quantity of milk = $\frac{4}{9}\times765$ = 340 litres

Initial quantity of water = $\frac{5}{9}\times765$ = 425 litres
If ‘y’ litres of milk is poured into the mixture, the ratio between quantity of milk and water will be 16:17 respectively.
$\frac{340+y}{425} = \frac{16}{17}$

$\frac{340+y}{25} = 16$

340+y = 400
y = 400-340 = 60
Hence, option b is the correct answer.

Question 19: In a mixture, the quantity of juice and water are in the ratio of 5:7 respectively. If 18 litres of juice is poured into the mixture, then the quantity of juice in the new mixture will be 25% less than the quantity of water in the new mixture. Find out the quantity of water in the mixture.

a) 637 litres

b) 560 litres

c) 504 litres

d) 651 litres

e) None of the above

19) Answer (C)

Solution:

In a mixture, the quantity of juice and water are in the ratio of 5:7 respectively.
Let’s assume the quantity of juice and water in the mixture are 5y and 7y respectively.
If 18 litres of juice is poured into the mixture, then the quantity of juice in the new mixture will be 25% less than the quantity of water in the new mixture.
$\frac{5y+18}{7y} = \frac{3}{4}$

20y+72 = 21y
21y-20y = y = 72
Quantity of water in the mixture = 7y = $7\times72$
= 504 litres
Hence, option c is the correct answer.

Question 20: In a drum, 1260 litres of pure milk is available. ‘Y’ litres of milk is taken out from the mixture and replaced with the water. This process is repeated once again after that the pure milk available in the drum is $1142\frac{6}{7}$ litres. Find out the value of ‘y’.

a) 45

b) 60

c) 75

d) 72

e) None of the above

20) Answer (B)

Solution:

$1142\frac{6}{7} = 1260 (1-\frac{y}{1260})^{2} $

$\frac{8000}{7} = 1260 (1-\frac{y}{1260})^{2} $

$\frac{8000}{7\times1260} = (1-\frac{y}{1260})^{2} $

$\frac{8000}{8820} = (1-\frac{y}{1260})^{2} $

$\frac{400}{441} = (1-\frac{y}{1260})^{2} $

$1-\frac{y}{1260} = \frac{20}{21}$

$\frac{1}{21} = \frac{y}{1260}$

y = 60
Hence, option b is the correct answer.

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