Online exam in Mixture and Allegations For Quantitative Aptitude for Competitive exams like IBPS BANK PO/Clerical,SBI,RRB,SSC,LIC,UPSC-CSAT,SCRA.MAT,CMAT,MBA,SNAP,CAT,NTSE,CLAT
Mixture and Allegations-Test 4
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Subject :- Quantitative Aptitude
Chapter :- Mixture and Allegations-Test 4
Questions :- 25
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A dishonest milkman professes to sell his milk at cost price, but he mixes it with
water and thereby gains 33(1/3)%. The percentage of water in the mixture is?
Correct
Ratio of water : milk can be found out as
Water: Milk=33(1/3):100 =1:3
hence water = 1/(1+4)*100=25%
Incorrect
Ratio of water : milk can be found out as
Water: Milk=33(1/3):100 =1:3
hence water = 1/(1+4)*100=25%
Question 2 of 25
2. Question
1 points
A person has a chemical of Rs 15 per litre. In what ratio should water be mixed in that
chemical so that after selling the mixture at Rs 12/litre he may get a profit of 20%.
Correct
With 20% profit, and SP=12,
CP=10
By alligation,
15 0
10
10 5
=>2:1
Incorrect
With 20% profit, and SP=12,
CP=10
By alligation,
15 0
10
10 5
=>2:1
Question 3 of 25
3. Question
1 points
If 2 kg of metal, of which 1/3 is zinc and the rest is copper be mixed with 3 kg of
metal of which ¼ is zinc and the rest is copper, What is the ratio of zinc to copper
in the mixture?
A man has 90 pens. He sells some of these at a profit of 15% and the rest at 9% profit.
On the whole transaction he gets a profit of 11%. How many pens did he sell at 9%
profit?
A butler stole wine from a butt of sherry which contained 35% spirit and he replaced
what he had stolen by wine containing only 20% spirit. The butt was then 25% strong
only. How much of the butt did he steal?
Correct
35% 20%
25%
5 10
=>1:2
The butt with alcohol of 35%=1/3 means
butler stole 1-1/3=2/3 part
Incorrect
35% 20%
25%
5 10
=>1:2
The butt with alcohol of 35%=1/3 means
butler stole 1-1/3=2/3 part
Question 6 of 25
6. Question
1 points
A container contains some amount of milk. A milkman adds 200 ml of water for each
one liter of milk in the container. 6 liters of the mixture is sold from the container and
10 liters 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.
Correct
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
Incorrect
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
Question 7 of 25
7. Question
1 points
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.
Correct
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
Incorrect
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
Question 8 of 25
8. Question
1 points
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?
Correct
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
Incorrect
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
Question 9 of 25
9. Question
1 points
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?
Correct
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
Incorrect
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
Question 10 of 25
10. Question
1 points
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.
Correct
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) = 18×2/25
Use options to check the answer.
Incorrect
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) = 18×2/25
Use options to check the answer.
Question 11 of 25
11. Question
1 points
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?
Correct
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
Incorrect
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
Question 12 of 25
12. Question
1 points
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?
Correct
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
Incorrect
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
Question 13 of 25
13. Question
1 points
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?
Correct
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
Incorrect
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
Question 14 of 25
14. Question
1 points
12 liters of water is drawn out from a container full of water and replaced by
milk. Again 12 liters 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?
Correct
Incorrect
Question 15 of 25
15. Question
1 points
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?
Correct
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
Incorrect
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
Question 16 of 25
16. Question
1 points
A 56 litre mixture contains milk and water in the ratio of 5 : 2 . How much water should be added to the mixture so as make the resultant mixture containing 40% water in it?
Correct
In 56 L, milk = 5/(5+2) * 56 = 40 L, so water
= 56 – 40 = 16 L
Final ratio of milk to water will be = 60 :
40 = 3 : 2
Let x litres of water to be added. So
40/(16+x) = 3/2
Solve, x = 32/3 L
Incorrect
In 56 L, milk = 5/(5+2) * 56 = 40 L, so water
= 56 – 40 = 16 L
Final ratio of milk to water will be = 60 :
40 = 3 : 2
Let x litres of water to be added. So
40/(16+x) = 3/2
Solve, x = 32/3 L
Question 17 of 25
17. Question
1 points
A mixture of 30 liters contains milk and water in the ratio 7 : 3. 10 liters of the mixture is taken out and replaced with pure milk and the same operation is repeated one more time. Find the final ratio of milk to water in the mixture.
Correct
In 30 L of mixture, milk = 7/10 * 30 = 21L,
so water = 9 L
let x = amount of water after replacement
and y = amount of water before
replacement, so y = 9
Now
x/y = [1 – 10/30]2
Solve, x = 4 L
Now since mixture is 30 l only after
replacement also. So milk in mixture after
replacement = 30 – 4 = 26 L
So final ratio = 26 : 4 = 13 : 2
Incorrect
In 30 L of mixture, milk = 7/10 * 30 = 21L,
so water = 9 L
let x = amount of water after replacement
and y = amount of water before
replacement, so y = 9
Now
x/y = [1 – 10/30]2
Solve, x = 4 L
Now since mixture is 30 l only after
replacement also. So milk in mixture after
replacement = 30 – 4 = 26 L
So final ratio = 26 : 4 = 13 : 2
Question 18 of 25
18. Question
1 points
How much milk (in liters) costing Rs 50 per liters should be mixed with 18 liters of
milk costing Rs 56 per liters so that there is a profit of 25% on selling the mixture at Rs
65 per liters?
Correct
CP of mixture = 100/125 * 65 = Rs 52
Let x L of milk to be mixed. So by method
of allegation:
(x)……………..…..(18)
50…………………..56
………….52
4……………………..2
So x/18 = 4/2
x = 36 L
Incorrect
CP of mixture = 100/125 * 65 = Rs 52
Let x L of milk to be mixed. So by method
of allegation:
(x)……………..…..(18)
50…………………..56
………….52
4……………………..2
So x/18 = 4/2
x = 36 L
Question 19 of 25
19. Question
1 points
A 24 litres of milk and water mixture contains milk and water in the ratio 3 : 5.
What litres of the mixture should be taken out and replaced with pure milk so that the
final mixture contains milk and water in equal proportions?
Correct
In 24 L of mixture, milk = 3/8 * 24 = 9 L, so
water = 15 L
Now since the mixture is to be replaced
with pure milk, the amount of mixture will
remain same after replacement too.
In 24 L mixture, to have 12 l water and 12 L
milk, 3 L of water should be taken out, since
we are only adding milk.
Let x L of mixture taken out. So 5/8 * x = 3,
Solve, x = 24/5 L
Incorrect
In 24 L of mixture, milk = 3/8 * 24 = 9 L, so
water = 15 L
Now since the mixture is to be replaced
with pure milk, the amount of mixture will
remain same after replacement too.
In 24 L mixture, to have 12 l water and 12 L
milk, 3 L of water should be taken out, since
we are only adding milk.
Let x L of mixture taken out. So 5/8 * x = 3,
Solve, x = 24/5 L
Question 20 of 25
20. Question
1 points
25 litres are drawn from a cask full of wine and is then filled with water. This operation
is performed one more time. The ratio of the quantity of wine now left in cask to that
of the water is 36 : 85. How much wine the cask hold originally?
Correct
Let x L wine was there originally. So
36/(36+85) = (1 – 25/x)2
Solve, x = 55 L
Incorrect
Let x L wine was there originally. So
36/(36+85) = (1 – 25/x)2
Solve, x = 55 L
Question 21 of 25
21. Question
1 points
Out of 2100 kg wheat, some part is sold making 10% profit while the remaining part is sold making 16% profit. If there is an overall profit of 14%, what quantity was sold at 16% profit?
Correct
By method of Alligation:
10………………..16
…………14
(16-14)…………..(14-10)
2……………….4
So 2 : 4 = 1 : 2
so part at 16% profit = 2/(1+2) * 2100 =
1400 kg
Incorrect
By method of Alligation:
10………………..16
…………14
(16-14)…………..(14-10)
2……………….4
So 2 : 4 = 1 : 2
so part at 16% profit = 2/(1+2) * 2100 =
1400 kg
Question 22 of 25
22. Question
1 points
Container A and B contains water and alcohol in the ratio 1 : 3 and 3 : 2
respectively. How much amount of mixture from container A should be mixed with 30 L of mixture from container B, so that the resultant mixture contains water and
alcohol in the ratio 11 : 12?
Correct
Water in A = 1/4. Water in B = 3/5 . And in
resultant =11/23
So by allegation method:
(x)…………….(30)
1/4………………..3/5
………..11/23
14/(23*5)…………..21/(23*4)
Take ratio: 14/23*5 : 21/23*4
Gives 8 : 15
So x/30 = 8/15
Solve, x = 16 L
Incorrect
Water in A = 1/4. Water in B = 3/5 . And in
resultant =11/23
So by allegation method:
(x)…………….(30)
1/4………………..3/5
………..11/23
14/(23*5)…………..21/(23*4)
Take ratio: 14/23*5 : 21/23*4
Gives 8 : 15
So x/30 = 8/15
Solve, x = 16 L
Question 23 of 25
23. Question
1 points
The rice sold by a shopkeeper contains 15% low quality rice. What quantity of good quality rice should be added to 70 kg of rice so that percentage of low quality wheat becomes 7%?
Correct
In good quality rice, there is 0% low quality rice
So method of allegation:
(70 kg)……………………(x kg)
15% …………………………0%
…………………..7%
7……………………………..8
So 7 : 8
Gives 70/x = 7/8
Solve, x = 80 kg
Incorrect
In good quality rice, there is 0% low quality rice
So method of allegation:
(70 kg)……………………(x kg)
15% …………………………0%
…………………..7%
7……………………………..8
So 7 : 8
Gives 70/x = 7/8
Solve, x = 80 kg
Question 24 of 25
24. Question
1 points
Container A and B contains 25% and 50% water respectively. The rest is milk in both
the containers. How much amount should be mixed from container A to some amount
in to some amount of container B so as to get 12 liters of new mixture having water to
milk ratio 3 : 5?
Correct
In resultant mixture, water is 3/8 * 100 =
75/2%
So by method of allegation:
25%……………………………50%
………………..75/2%
25/2%……………………….25/2%
so ratio is 25/2 : 25/2 = 1 : 1
And the total should be 12 l, so 6 l of
mixture from A, and 6 l from B.
Incorrect
In resultant mixture, water is 3/8 * 100 =
75/2%
So by method of allegation:
25%……………………………50%
………………..75/2%
25/2%……………………….25/2%
so ratio is 25/2 : 25/2 = 1 : 1
And the total should be 12 l, so 6 l of
mixture from A, and 6 l from B.
Question 25 of 25
25. Question
1 points
A mixture contains A and B in the ratio of 5 : 3. 16 litres of this mixture is taken out
and 5 litres of A is poured in. the new mixture has ratio of A to B as 11 : 6. Find
the total original quantity of mixture.
Correct
A = 5x, B = 3x
16 l taken out, so let total mixture now = 5x
+ 3x + 16 = 8x + 16
Now 5 l of A poured in and then ratio
becomes 11 : 6
So (5x+5)/3x = 11/6
Solve, x = 10
So total mixture originally = 8x + 16 =
8*10 + 16 = 96 litres
Incorrect
A = 5x, B = 3x
16 l taken out, so let total mixture now = 5x
+ 3x + 16 = 8x + 16
Now 5 l of A poured in and then ratio
becomes 11 : 6
So (5x+5)/3x = 11/6
Solve, x = 10
So total mixture originally = 8x + 16 =
8*10 + 16 = 96 litres