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A jar is full of whiskey contains 40% alcohol. A part of this whiskey is replaced by another containing 19% alcohols and now the percentage of alcohol was found to be 26%. The quantity of whiskey replaced is:
a)4/3
b)3/4
c)3/2
d)2/3
Correct answer is option 'D'. Can you explain this answer?
|
Pritam Joshi answered |
A thief steals four gallons of liquid soap kept in a train compartment’s bathroom from a container that is full of liquid soap. He then fills it with water to avoid detection. Unable to resist the temptation he steals 4 gallons of the mixture again, and fills it with water. When the liquid soap is checked at a station it is found that the ratio of the liquid soap now left in the container to that of the water in it is 36 : 13. What was the initial amount of the liquid soap in the container if it is known that the liquid soap is neither used nor augmented by anybody else during the entire period?- a)7 gallons
- b)14 gallons
- c)21 gallons
- d)28 gallons
Correct answer is option 'D'. Can you explain this answer?
A thief steals four gallons of liquid soap kept in a train compartment’s bathroom from a container that is full of liquid soap. He then fills it with water to avoid detection. Unable to resist the temptation he steals 4 gallons of the mixture again, and fills it with water. When the liquid soap is checked at a station it is found that the ratio of the liquid soap now left in the container to that of the water in it is 36 : 13. What was the initial amount of the liquid soap in the container if it is known that the liquid soap is neither used nor augmented by anybody else during the entire period?
a)
7 gallons
b)
14 gallons
c)
21 gallons
d)
28 gallons
|
KS Coaching Center answered |
It can be seen from the ratio 36:13 that the proportion of liquid soap to water is 36/49 after two mixings. This means that 6/7th of the liquid soap must have been allowed to remain in the container and hence l/7th of the conatiner’s original liquid soap would have been drawn out by the thief. Since he takes out 4 gallons every time, there must have been 28 gallons in the container. ( as 4 should be l/7th of 28)
A mixture of 100 litres of spirit and alcohol contains 25% alcohol. How much more alcohol should be added to the mixture to increase the percentage of alcohol to 30% in the new mixture?
- a)3.33 litres
- b)7.14 litres
- c)5 litres
- d)4 litres
Correct answer is option 'B'. Can you explain this answer?
A mixture of 100 litres of spirit and alcohol contains 25% alcohol. How much more alcohol should be added to the mixture to increase the percentage of alcohol to 30% in the new mixture?
a)
3.33 litres
b)
7.14 litres
c)
5 litres
d)
4 litres
|
Kavya Sharma answered |
Alcohol content in the alcohol to be added = 100%
Therefore, the allegation diagram for this problem can be drawn as:
Therefore, the allegation diagram for this problem can be drawn as:
Therefore, ratio of the mixture to alcohol = 70/5 = 14/1
So, alcohol to be added = 100/14
So, alcohol to be added = 100/14
Hence, the answer is "7.14 litres".
Choice B is the correct answer.
In what ratio must rice at Rs.7.10 be mixed with rice at Rs.9.20 so that the mixture may be worth Rs.8 per Kg?
- a)5 : 4
- b)2 : 1
- c)3 : 2
- d)4 : 3
Correct answer is option 'D'. Can you explain this answer?
a)
5 : 4
b)
2 : 1
c)
3 : 2
d)
4 : 3
|
Dhruv Mehra answered |
By the rule of alligation, we have
Two containers of equal capacity are full of a mixture of oil and water. In the first, the ratio of oil to water is 4 : 7 and in the second it is 7 : 11. Now both the mixtures are mixed in a bigger container. What is the resulting ratio of oil to water?- a)149 : 247
- b)247 : 149
- c)143 : 241
- d)241 : 143
Correct answer is option 'A'. Can you explain this answer?
Two containers of equal capacity are full of a mixture of oil and water. In the first, the ratio of oil to water is 4 : 7 and in the second it is 7 : 11. Now both the mixtures are mixed in a bigger container. What is the resulting ratio of oil to water?
a)
149 : 247
b)
247 : 149
c)
143 : 241
d)
241 : 143
|
Future Foundation Institute answered |
Assume the capacity of the two containers is 198 liters each. When we mix 198 liters of the first and 198 liters of the second the amount of oil would be: 198 x 4/11 + 198 x 7/18 = 72 + 77 = 149 liters. Consequently the amount of water would be 396 - 149 = 247 liters. Option (a) is correct.
8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of the water is 16:65. How much wine did the cask originally hold?
- a)30 litres
- b)26 litres
- c)24 litres
- d)32 litres
Correct answer is option 'C'. Can you explain this answer?
8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of the water is 16:65. How much wine did the cask originally hold?
a)
30 litres
b)
26 litres
c)
24 litres
d)
32 litres
|
Arya Roy answered |
8 litres are drawn from a cask full of wine and is then filled with water.
This operation is performed three more times.
The ratio of the quantity of wine now left in cask to that of the water is 16 ∶ 65
Calculations:
Calculations:
Let the quantity of the wine in the cask originally be x litres.
After first operation, wine left in the cask = (x - 8) litres So, the ratio of the quantity of wine now left in cask to that of filled cask = 
This operation is performed three more times. Then, Wine : Water = 16 : 65 or wine : water = 16 : (16 + 65) = 81
Correct answer is 24.
A merchant purchased two qualities of pulses at the rate of Rs. 200 per quintal and Rs. 260 per quintal. In 52 quintals of the second quality, how much pulse of the first quality should be mixed so that by selling the resulting mixture at Rs. 300 per quintal, he gains a profit of 25%?- a)100 quintals
- b)104 quintals
- c)26 quintals
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
A merchant purchased two qualities of pulses at the rate of Rs. 200 per quintal and Rs. 260 per quintal. In 52 quintals of the second quality, how much pulse of the first quality should be mixed so that by selling the resulting mixture at Rs. 300 per quintal, he gains a profit of 25%?
a)
100 quintals
b)
104 quintals
c)
26 quintals
d)
None of these
|
|
KS Coaching Center answered |
By selling at 300 if we need to get a profit of 25% it means that the cost price would be 300/1.25 = 240.
Thus, in 52 quintals of the second we need to mix 26 quintals of the first.
How many kilograms of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per Kg so that there may be a gain of 10 % by selling the mixture at Rs. 9.24 per Kg ?
- a)60 Kg
- b)63 kg
- c)58 Kg
- d)56 Kg
Correct answer is option 'B'. Can you explain this answer?
a)
60 Kg
b)
63 kg
c)
58 Kg
d)
56 Kg
|
Pallabi Deshpande answered |
C.P. of 1 kg sugar of 1st kind C.P. of 1 kg sugar of 2nd kind
Therefore, Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3.
Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind.
Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg.
Two types of oils having the rates of Rs. 4/kg and Rs. 5/kg respectively are mixed in order to produce a mixture having the rate of Rs. 4.60/kg. What should be the amount of the second type of oil if the amount of the first type of oil in the mixture is 40 kg?- a)75 kg
- b)50 kg
- c)60 kg
- d)40 kg
Correct answer is option 'C'. Can you explain this answer?
Two types of oils having the rates of Rs. 4/kg and Rs. 5/kg respectively are mixed in order to produce a mixture having the rate of Rs. 4.60/kg. What should be the amount of the second type of oil if the amount of the first type of oil in the mixture is 40 kg?
a)
75 kg
b)
50 kg
c)
60 kg
d)
40 kg
|
Ravi Singh answered |
Mixing Rs. 4/kg and Rs. 5/kg to get Rs. 4.6 per kg we get that the ratio of mixing is 2:3. If the first oil is 40 kg, the second would be 60 kg
Hence, by the rule of allegation they must be mixed in the ratio 40:60
if quantity of first type is 40kg , the quantity of second type will be 60 kg
if quantity of first type is 40kg , the quantity of second type will be 60 kg
Practice Quizzes or MCQ (Multiple Choice Questions) with solution are available for Practice, which would help you prepare for Alligation or Mixture under Quantitative Aptitude. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations. Q. A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?- a)26 litres
- b)29.16 litres
- c)28 litres
- d)28.2 litres
Correct answer is option 'B'. Can you explain this answer?
Practice Quizzes or MCQ (Multiple Choice Questions) with solution are available for Practice, which would help you prepare for Alligation or Mixture under Quantitative Aptitude. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations.
Q. A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?
a)
26 litres
b)
29.16 litres
c)
28 litres
d)
28.2 litres
|
Raghavendra Sharma answered |
40M
After replacing
36M : 4W => 9:1
In the next replacement
Out of 4 Litres mixture
3.6L milk, 0.4L Water
Now, Milk => 32.4, Water => 7.6
i.e 4.26 : 1 => The current ratio of the mixture
Next 4 Litres in the above ratio
4/5.26= 0.76
0.76x4.26 = 3.239 (3.24)
32.4–3.24= 29.16 Litres of Milk
A sum of Rs. 36.90 is made up of 90 coins that are either 20 paise coins or 50 paise coins. Find out how many 20 paise coins are there in the total amount,- a)47
- b)43
- c)27
- d)63
Correct answer is option 'C'. Can you explain this answer?
A sum of Rs. 36.90 is made up of 90 coins that are either 20 paise coins or 50 paise coins. Find out how many 20 paise coins are there in the total amount,
a)
47
b)
43
c)
27
d)
63
|
Aryan Khanna answered |
Let coins of 20 paisa be x
and let coins of 50 paisa be y
convert the 36. 90 RS in paisa
it will be 3690 paisa
means
20x+50y=3690 ... (1)
x+y=90 ... (2)
multiply (2) by 50 on both sides we get
50x+50y=4500
subtract (2) from (1)
20x+50y=3690
50x+50y=4500
-30x=-810
x=-810/-30
x=27
the number of coins of 20 paisa are 27
The cost of Type 1 material is Rs. 15 per kg and Type 2 material is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then what is the price per kg of the mixed variety of material?- a)Rs. 19
- b)Rs. 16
- c)Rs. 18
- d)Rs. 17
Correct answer is option 'C'. Can you explain this answer?
The cost of Type 1 material is Rs. 15 per kg and Type 2 material is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then what is the price per kg of the mixed variety of material?
a)
Rs. 19
b)
Rs. 16
c)
Rs. 18
d)
Rs. 17
|
Ishani Rane answered |
Let the price of the mixed variety be Rs. x per kg.
By rule of alligation, we have:
Therefore, (20 - x)/(x - 15) = 2/3
=> 60 - 3x = 2x - 30
=> 5x = 90
=> x = 18
Two vessels A and B contain spirit and water in the ratio 5 : 2 and 7 : 6 respectively. Find the ratio in which these mixture be mixed to obtain a new mixture in vessel C containing spirit and water in the ration 8 : 5 ?
- a)3: 4
- b)4 : 3
- c)9 : 7
- d)7 : 9
Correct answer is option 'D'. Can you explain this answer?
a)
3: 4
b)
4 : 3
c)
9 : 7
d)
7 : 9
|
Manoj Ghosh answered |
Spirit in 1 litre mix of A = 5/7 litre.
Spirit in 1 litre mix of B = 7/13 litre.
Spirit in 1 litre mix of C = 8/13 litre.
By rule of alligation we have required ratio X:Y
X : Y
5/7 7/13
\ /
(8/13)
/ \
(1/13) : (9/91)
7 9
Therefore required ratio = 1/13 : 9/91
= 7:9
A vessel is full of refined oil. 1/4 of the refined oil is taken out and the vessel is filled with mustard oil. If the process is repeated 4 times and 10 litres of refined oil is finally left in the vessel, what is the capacity of the vessel?
a)33 litresb)2460/41 litresc)2560/81 litresd)30 litresCorrect answer is option 'C'. Can you explain this answer?
|
|
KS Coaching Center answered |
Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety of tea in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, what is the price of the third variety per kg ?
- a)Rs.182.50
- b)Rs.170.5
- c)Rs.175.50
- d)Rs.180
Correct answer is option 'C'. Can you explain this answer?
a)
Rs.182.50
b)
Rs.170.5
c)
Rs.175.50
d)
Rs.180
|
|
Manoj Ghosh answered |
Since first and second varieties are mixed in equal proportions.
So, their average price = Rs. 126 + 135/2 = Rs. 130.50
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
By the rule of alligation, we have:
x - 153 = 22.50
x = 175.50
In the Singapore zoo, there are deers and there are ducks. If the heads are counted, there are 180, while the legs are 448. What will be the number of deers in the zoo?- a)136
- b)68
- c)44
- d)22
Correct answer is option 'C'. Can you explain this answer?
In the Singapore zoo, there are deers and there are ducks. If the heads are counted, there are 180, while the legs are 448. What will be the number of deers in the zoo?
a)
136
b)
68
c)
44
d)
22
|
|
Aryan Khanna answered |
Let x be the number of deers in the zoo
Then (180-x)be the number of ducks, as each animal and bird has one head.
Now duck has 2 legs and deer has 4 legs so
4x+2(180-x)=448
2x+360=448
X=44
Then (180-x)be the number of ducks, as each animal and bird has one head.
Now duck has 2 legs and deer has 4 legs so
4x+2(180-x)=448
2x+360=448
X=44
No of deers=44
The price of a pen and a pencil is Rs. 35. The pen was sold at a 20% profit and the pencil at a 10% loss. If in the transaction a man gains Rs. 4, how much is cost price of the pen?- a)Rs. 10
- b)Rs. 25
- c)Rs. 20
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
The price of a pen and a pencil is Rs. 35. The pen was sold at a 20% profit and the pencil at a 10% loss. If in the transaction a man gains Rs. 4, how much is cost price of the pen?
a)
Rs. 10
b)
Rs. 25
c)
Rs. 20
d)
None of these
|
|
Ravi Singh answered |
Solve using options as that would be the best way to tackle this question. Option (b) fits the situation perfectly as if we take the price of the pen as Rs. 25, the cost of the pencil would be Rs. 10. The profit in selling the pen would be Rs.5 while the loss in selling the pencil would be Rs. 1. The total profit would be Rs. 4 as stipulated by the problem.
A mixture of 125 gallons of wine and water contains 20% water. How much water must be added to the mixture in order to increase the percentage of water to 25% of the new mixture?- a)10 gals
- b)8.5 gals
- c)8 gals
- d)8.33 gals
Correct answer is option 'D'. Can you explain this answer?
A mixture of 125 gallons of wine and water contains 20% water. How much water must be added to the mixture in order to increase the percentage of water to 25% of the new mixture?
a)
10 gals
b)
8.5 gals
c)
8 gals
d)
8.33 gals
|
|
Aaditya Yadav answered |
In 125 gallons we have 25 gallons water and 100 gallons wine. To increase the percentage of water to 25%, we need to reduce the percentage of wine to 75%. This means that 100 gallons of wine = 75% of the new mixture. Thus the total mixture = 133.33 gallons. Thus, we need to mx 133.33 - 125 = 8.33 gallons of water in order to make the water equivalent to 25% of the mixture.
A mixture of 70 litres of alcohol and water contains 10% of water. How much water must be added to the above mixture to make the water 12.5% of the resulting mixture?- a)1 litre
- b)1.5 litre
- c)2 litres
- d)2.5 litres
Correct answer is option 'C'. Can you explain this answer?
A mixture of 70 litres of alcohol and water contains 10% of water. How much water must be added to the above mixture to make the water 12.5% of the resulting mixture?
a)
1 litre
b)
1.5 litre
c)
2 litres
d)
2.5 litres
|
|
Ishani Rane answered |
Mixture = 70 L
Water =10% of mixture = 10% of 70 = 7 L.
Alcohol = 63 L.
Let x water added. Now, Water and Alcohol ratio will be,
(7 + x)/63 = 12.5/87.5
7 +x = 787.5/87.5
7 + x = 9
x = 2 L.
Water added = 2 L.
There are two mixtures of honey and water, the quantity of honey in them being 25% and 75% of the mixture. If 2 gallons of the first are mixed with three gallons of the second, what will be the ratio of honey to water in the new mixture?- a)11 : 2
- b)11 :9
- c)9 : 11
- d)2 : 11
Correct answer is option 'B'. Can you explain this answer?
There are two mixtures of honey and water, the quantity of honey in them being 25% and 75% of the mixture. If 2 gallons of the first are mixed with three gallons of the second, what will be the ratio of honey to water in the new mixture?
a)
11 : 2
b)
11 :9
c)
9 : 11
d)
2 : 11
|
|
Arya Roy answered |
In what ratio must tea at Rs.62 per Kg be mixed with tea at Rs. 72 per Kg so that the mixture must be worth Rs. 64.50 per Kg?
- a)1 : 2
- b)2 : 1
- c)3 : 1
- d)1 : 3
Correct answer is option 'C'. Can you explain this answer?
a)
1 : 2
b)
2 : 1
c)
3 : 1
d)
1 : 3
|
|
Raghavendra Sharma answered |
C.P of a unit quantity of 1st kind = Rs. 62
C.P of a unit quantity of 2nd kind = Rs. 72
Mean price = Rs. 64.50
Required ratio = 7.50 : 2.50 = 3 : 1
400 students took a mock exam in Delhi. 60% of the boys and 80% of the girls cleared the cut off in the examination. If the total percentage of students qualifying is 65%, how many girls appeared in the examination?- a)100
- b)120
- c)150
- d)300
Correct answer is option 'A'. Can you explain this answer?
400 students took a mock exam in Delhi. 60% of the boys and 80% of the girls cleared the cut off in the examination. If the total percentage of students qualifying is 65%, how many girls appeared in the examination?
a)
100
b)
120
c)
150
d)
300
|
Naroj Boda answered |
The ratio of boys and girls appearing for the exam can be seen to be 3:1 using the following alligation figure.
This means that out of 400 students, there must have been 100 girls who appeared in the exam.
A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?
- a)5 litres, 7 litres
- b)7litres, 4 litres
- c)6litres, 6 litres
- d)4litres, 8 litres
Correct answer is option 'C'. Can you explain this answer?
a)
5 litres, 7 litres
b)
7litres, 4 litres
c)
6litres, 6 litres
d)
4litres, 8 litres
|
|
Ishani Rane answered |
Let x and (12-x) litres of milk be mixed from the first and second container respectively
Amount of milk in x litres of the the first container = .75x
Amount of water in x litres of the the first container = .25x
Amount of milk in (12-x) litres of the the second container = .5(12-x)
Amount of water in (12-x) litres of the the second container = .5(12-x)
Ratio of water to milk = [.25x + .5(12-x)] : [.75x + .5(12-x)] = 3 : 5
⇒ (.25x+6-5x)/(.75x+6-.5x) =3/5
⇒(6−.25x)/(.25x+6) =3/5
⇒30−1.25x=.75x+18
⇒2x=12
⇒x=6
Since x = 6, 12-x = 12-6 = 6
Hence 6 and 6 litres of milk should mixed from the first and second container respectively
A container contains a mixture of two liquids P and Q in the ratio 7 : 5. When 9 litres of mixture are drawn off and the container is filled with Q, the ratio of P and Q becomes 7 : 9. How many litres of liquid P was contained in the container initially?
- a)23
- b)21
- c)19
- d)17
Correct answer is option 'B'. Can you explain this answer?
a)
23
b)
21
c)
19
d)
17
|
Gowri Chakraborty answered |
A vessel is filled with liquid, 3 parts of which are water and 5 parts of syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup? - a)1/3
- b)1/4
- c)1/5
- d)1/6
Correct answer is option 'C'. Can you explain this answer?
A vessel is filled with liquid, 3 parts of which are water and 5 parts of syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
a)
1/3
b)
1/4
c)
1/5
d)
1/6
|
|
Raghavendra Sharma answered |
A cistern contains 50 litres of water. 5 litres of water is taken out of it and replaced by wine. The process is repeated again. Find the proportion of wine and water in the resulting mixture.- a)1 : 4
- b)41 : 50
- c)19 : 81
- d)81 : 19
Correct answer is option 'C'. Can you explain this answer?
A cistern contains 50 litres of water. 5 litres of water is taken out of it and replaced by wine. The process is repeated again. Find the proportion of wine and water in the resulting mixture.
a)
1 : 4
b)
41 : 50
c)
19 : 81
d)
81 : 19
|
Poulomi Sarkar answered |
Amount of water left = 50 x 9/10 x 9/10 = 40.5 liters. Hence, wine = 9.5 liters. Ratio of wine and water = 19:81. Option (c) is correct.
The average salary per head of all employees of a company is Rs. 600. The average salary of 120 officers is Rs. 4000. If the average salary per head ofthe rest of the employees is Rs. 560, find the total number of workers in the company.- a)10200
- b)10320
- c)10500
- d)10680
Correct answer is option 'B'. Can you explain this answer?
The average salary per head of all employees of a company is Rs. 600. The average salary of 120 officers is Rs. 4000. If the average salary per head ofthe rest of the employees is Rs. 560, find the total number of workers in the company.
a)
10200
b)
10320
c)
10500
d)
10680
|
|
Gowri Chakraborty answered |
Total no. of workers be x
Their average salary = Rs 600
Total salary of all workers = 600x
Average salary of 120 officers = Rs 4000
Total salary of 120 officers = 120 x 4000 = Rs 48000
Average salary of rest of employees = Rs 560
Total salary of these rest of employees = (x - 120)x560
⇒ (x - 120)x560 + 48000 = 600x
⇒56x - 672 + 4800 = 600x
⇒ 4x = 4184
⇒ x = 10320
Total number of workers in the factory = 10320
A vessel is full of a mixture of kerosene and petrol in which there is 18% kerosene. Eight litres are drawn off and then the vessel is filled with petrol. If the kerosene is now 15%, how much does the vessel hold?- a)40 litres
- b)32 litres
- c)36 litres
- d)48 litres
Correct answer is option 'D'. Can you explain this answer?
A vessel is full of a mixture of kerosene and petrol in which there is 18% kerosene. Eight litres are drawn off and then the vessel is filled with petrol. If the kerosene is now 15%, how much does the vessel hold?
a)
40 litres
b)
32 litres
c)
36 litres
d)
48 litres
|
|
Ishani Rane answered |
kerosene=18%
so petrol =82%
after kerosene =15%
petrol=85%
so 3% =8
lit so total kerosene in the mixture =(8*18/3) =48 lit
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