# Quantitative Aptitude: Mixture and Alligation Set 2

Mixture and Alligation Questions for Banking and Insurance Exams.

1. A container contains some amount of milk. A milkman adds 200 ml of water for each one litre of milk in the container. 6 litres of the mixture is sold from the container and 10 litres of milk is added to the remaining mixture. If now the ratio of milk to water in container is 25 : 3, find the initial quantity of milk in the container.
A) 26 l
B) 29 l
C) 30 l
D) 20 l
E) None of these
Option D
Solution
:
Let initial quantity of milk = 10x litres, For each 1 litre, 200 ml of water is added, so after adding water, quantity of mixture become = 12x litres
Now 6 l of mixture is sold, and 10 l of milk is added
So remaining quantity is (12x – 6 +10) = (12x + 4)
In this final quantity, milk = 10x – (10x/12x * 6) + 10 = (10x + 5)
So (10x+5)/(12x +4) = 25/(25+3)
Solve, x = 2
So initial quantity of milk = 10x = 20 litres
2. A container contains 64 litres of pure milk. One-fourth of the milk is replaced by water. Again the operation is performed, and one-fourth of mixture is replaced by water. Find the final ratio of milk to water in the container.
A) 11 : 8
B) 10 : 7
C) 9 : 7
D) 10 : 9
E) 12 : 7
Option C
Solution
:
After 2 operations, final quantity of milk = 64 (1 – 1/4)2 = 36 litres
So quantity of water is 64  – 36 = 28 l
So ratio is 36 : 28 = 9 : 7
3. In what ratio do the three varieties of rice costing Rs 6, Rs 8 and Rs 9 per 100 grams should be mixed in order to obtain a mixture costing Rs 84 per kg?
A) 2 : 3 : 4
B) 1 : 3 : 6
C) 1 : 2 : 5
D) 3 : 4 : 2
E) None of these
Option B
Explanation
:
Rs 6, Rs 8 and Rs 9 per 100 grams  means Rs Rs 60, Rs 80 and Rs 90 per kg
84 is middle number between 80 and 90
So take ratios as:
60…………………..90
……………84
6…………………..24
Ratio is 6 : 24 = 1: 4
AND
80…………………..90
……………84
6…………………..4
Ratio is 6 : 4 = 3: 2
So final ratio is 1 : 3 : (4+2) = 1: 3: 6
4. Two containers A and B contain mixture of milk and water such that A contains 40% milk and B contains 22% milk. Some part of mixture in container A is replaced by equal quantity of mixture from container B. How much quantity of the mixture was replaced if final mixture contains 32% milk?
A) 3/7
B) 2/5
C) 7/10
D) 4/7
E) 5/9
Option E
Solution
:
By the method allegation:
Reaming……………….Replaced
22………………………….…..40
…………….…..32
8……………………..………..10
So ratio is 8 : 10 = 4 : 5
So replaced part is 5/(4+5) = 5/9
5. A container filled of milk-water mixture contains 75% milk. 5 litres of this mixture is replaced by water. Next, 10 l of the mixture is replaced by water. If the final percentage of milk in the container is 54%, find the initial quantity of mixture in the container.
A) 50 l
B) 40 l
C) 60 l
D) 70 l
E) 55 l
Option A
Solution
:
Let initial quantity of mixture = x l
initial quantity of milk = 0.75x l
So 0.75x (1 – 5/x) (1 – 10/x) = 0.54 x
Solve, (x-5)(x-10) = 18x2/25
Use options to check the answer.

6. How much milk (in litres) costing Rs 60 per litres should be mixed with 35 litres of milk costing Rs 84 per litres so that there is a profit of 50% on selling the mixture at Rs 111 per litres?
A) 25 l
B) 32 l
C) 17 l
D) 36 l
E) 46 l
Option A
Solution:

CP of mixture = 100/150 * 111 = Rs 74
Let x l of milk to be mixed. So by method of allegation:
(x)……………..…..(35)
60…………………..84
………….74
10……………………..14
So ratio is 10 : 14 = 5 : 7
So x/35 = 5/7
x = 25 l
7. A container whose capacity is 60 l contains milk and water in the ratio 3 : 2. How much quantity of the mixture should be replaced with pure milk so that in the final mixture, ratio of milk to water is 7 : 3?
A) 22 l
B) 20 l
C) 15 l
D) 17 l
E) 14 l
Option C
Solution:

In 60 l of mixture, milk = 3/5 * 60  = 36 l, so water = 24 l
Let x litres of mixture is replaced
So
Remaining Milk after replacement is = 36 – (3/5)*x + x = 36 + 2x/5
So  (36 + 2x/5)/60 = 7/10
Solve, x = 15 l
8. 3 containers having capacities in the ratio 2 : 3 : 1 contain mixture of liquids A and B such that the ratio of A to B in them is 2 : 3, 1 : 4 and 3 : 7 respectively. If all the three containers are emptied in a single container, what will be the ratio of A to B in the final mixture?
A) 13 : 58
B) 11 : 54
C) 22: 13
D) 17 : 43
E) None of these
Option D
Solution
:
2+3 = 5, 1+4 = 5, 3+ 7 = 10
LCM pf 5, 5, 10 = 10
Capacities are in the ratio 2 : 3 : 1
Suppose the capacities are 20, 30 and 10
So A in final mixture is 2/5 * 20 + 1/5 * 30 + 3/10 * 10 = 17
And B in final mixture is (20+30+10) – 17 = 43
So final ratio = 17 : 43
9. 12 litres of water is drawn out from a container full of water and replaced by milk. Again 12 litres of mixture are drawn and the container is again filled with milk. The ratio of final quantity of water to milk in the container is 11 : 25. How much did the container hold?
A) 60 litres
B) 65 litres
C) 72 litres
D) 39 litrers
E) None of these
Option C
Solution:

Let x litres is total capacity of container
Using formula, amount of water left = x [1 – 12/x]<sup>2</sup>
[1 – 12/x]<sup>2</sup>/x = 25/(25+11)
Solving we get, x = 72 l
10. There are two mixtures such that they contain 75% milk and 80% milk respectively. Some amount from first mixture is mixed with twice the same amount of second mixture. Find the percentage of milk in the resultant mixture?
A) 90.2%
B) 75.9%
C) 84.5%
D) 76.3%
E) 78.3%
Option E
Solution:

Let x from first mixture, then 2x form second
So milk from first = (75/100)*x, milk from second = (80/100)*2x
So milk in resultant mixture is (75x/100) + (160x/100) = 2.35x
Total mixture in third is x+2x = 3x
So % of milk is (2.35x/3x)*100

## 16 Thoughts to “Quantitative Aptitude: Mixture and Alligation Set 2”

1. •?((¯°·._.• ąkduuu •._.·°¯))؟•

mam last ques’s ans is not showing

1. Shubhra

now see

1. •?((¯°·._.• ąkduuu •._.·°¯))؟•

yes mam

2. •?((¯°·._.• ąkduuu •._.·°¯))؟•

mam uska ans 78.33 % ayega plz check

1. Shubhra

Yes

2. •?((¯°·._.• ąkduuu •._.·°¯))؟•

mam ?????? are u here

1. Shubhra

Yes?

1. •?((¯°·._.• ąkduuu •._.·°¯))؟•

nothing mam i had a doubt…. now clear ..thanku 🙂

2. •?((¯°·._.• ąkduuu •._.·°¯))؟•

meko ratio main doubt tha mujhe lga use ratio ke jese parallel main likhte hain :pp ab pta chla add karte hain 3rd ques

1. Shubhra

Ok ok

1. aspirant

mam in Q.8 So A in final mixture is 2/5 * 20 + 1/5 * 30 + 3/10 * 10 = 17 not 15,,3/7*10 nhi hona chaiye

2. Shubhra

Yes 3/10

3. Jellyfish

Thx 7/10

4. golden girl

thanku mam 🙂

5. Amit Kumar Singh

Question no.9

6. garima shah

mam 7th ko agar alligation se krte h to mera wrong kyo aa rha h….find btaiye…..
60LT…………………….?
M:W M:W

3:2 1:0
60% 100%

MEAN(M:W)
70%:30%
70%

3 1
NOW IF 3—->60 SO 1—–>30LT NHI HOGA KYA……PLS CORRECT ME WHERE I M WRONG.