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# 7/17/2014 Alligation Rule | Aptitude Questions with Answers and Explanations

http://www.campusgate.co.in/2011/10/alligation-rule.html 1/5
Alligation rule helps us to find, in what ratio two mixtures with different concentrations are to be mixed to
get a target concentration.
Assume that in an engineering college ECE branch average aggregte is 80% and that of CSE is 68%. In
what ratio the students in these classes are to be mixed to get an aggregate of 76%?
Take ECE class average as , CSE class average as . If there are students in ECE and students
in CSE then the overall average is calculated as follows
If we re arrange this equation
To apply this rule easily we follow a small diagram
Eventhough alligation rule is widely applied in mixtures, we can see this rule in many areas across arithmetic
Practice Problems
1. A person covers 800km partly at a speed of 50kmph and partly at a speed of 150kmph, in 10 hours over
all. What is the distance covered at the speeds of 150 kmph?
His average speed for the entire journey is
Now we need to find in what ratio he needs to travel 800km, partly at 50kmph, and 150kmph to get
average speed of 80kmph
lligation Rule
A
1
A
2
n
1
n
2
A
avg
=
× + × n
1
A
1
n
2
A
2
+ n
1
n
2
A
avg
× + × = × ( + ) n
1
A
1
n
2
A
2
A
avg
n
1
n
2
× ( − ) = × ( − ) n
2
A
2
A
avg
n
1
A
avg
A
1
=
n
1
n
2
( − ) A
2
A
avg
( − ) A
avg
A
1
= 80
800
10
7/17/2014 Alligation Rule | Aptitude Questions with Answers and Explanations
http://www.campusgate.co.in/2011/10/alligation-rule.html 2/5
So for every 70 parts of the time travelled at 50kmph, he has to travel 30 parts are 150kmph.
As the total time is 10 hours he must have travelled = 10 hours at 150 kmph
2. The cost of oil is Rs.100 per kilogram. After adulteration with another oil, which costs Rs.50 per kilogram,
Ram sells the mixture at Rs.96 per kilogram making a profit of 20%. In what rati does he mix the two kinds
of oil?
Before applying the alligation rule we need to make sure that all the perameters are in the same units.
Here 2 costs prices and 1 selling price was given. So we should conver the selling price into cost price.
Given

Now we apply the alligation rule.
So These two must be mixed in the ratio 3:2.
3. Two solutions of milk and water are combined in the ratio 2:3 by volume. The resultant solution is a
40% milk solution. Find the milk concentration in the first solution if the concentration of milk in the second
is 60%?
It was given that are in the ratio 2:3 and second solution concentration is 60 and resultant
solution concentration is 40.
× 30
30
70 + 30
C. P × (100 + 20)% = 96
⇒C. P =
96
120%
⇒C. P = ⇒96 × = 80
96
120
100
100
120
: n
1
n
2
7/17/2014 Alligation Rule | Aptitude Questions with Answers and Explanations
http://www.campusgate.co.in/2011/10/alligation-rule.html 3/5
From the above we know that 20, 40 - x must be in the ratio 2: 3
4. A shopkeeper sold 45 kg.of goods. If he sells some quantity at a loss of 3% and rest at 17% profit,
making 5% profit on the whole, find the quantity sold at profit.
Note: 17 - 5 = 12, and 5 - (-3) = 5 + 3 = 8
Therefore, Ratio of quantities sold at profit and at loss = 8 : 12 = 2 : 3
Therefore, Quantity sold at profit = x 45 = 18 kg.
5. A mixture of 70 litres of wine and water contains 10% water. How much water should be added to make
25% water in the resulting mixture?
Therefore, The ratio is 75 : 15 = 5 : 1.
Therefore, For every 5 litres of mixture, 1 litre of water is added.
Therefore, For 70 litres, water to be added = x 70 = 14 litres.
Alternative Method:
Water = 10% of 70 litres = 7 litres
⇒ = ⇒x = 10
20
40 − x
2
3
2
5
1
5
7/17/2014 Alligation Rule | Aptitude Questions with Answers and Explanations
http://www.campusgate.co.in/2011/10/alligation-rule.html 4/5
Wine = 70 - 7 = 63 litres
Now, in the new mixture, water is 25% and wine is 75%.
Hence, in new mixture wine is 3 times of water.
Therefore, Water in new mixture = x 63 = 21 litres
Therefore, Water to be added = 21 - 7 = 14 litres
6. A man purchased a horse and a cow for Rs. 5000. He sells the horse at 20% profit and the cow at 10%
loss. If he gains 2% on the whole transaction, the cost of the horse is:
Therefore, Ratio between cost of a horse and that of a cow = 12 : 18 = 2 : 3.
Therefore, Cost of the horse = x 5000 = Rs. 2000
7. In an examination, a student gets 3 marks for every correct answer and loses 1 mark for every wrong
answer. If he scores '0' marks in a paper of 100 questions, how many of his answers were correct?
Therefore, Ratio of correct and wrong answers = 1 : 3
Therefore, Correct answers = x 100 = 25
8. The batting average of a cricket player is 72 runs per inning. In the next 4 inning, he could score only 80
runs and thereby decreases his batting average by 2 runs. What is total number of inning played by him till
last match?
Average of last 4 inning = = 20 runs
Average of inning played earlier = 72 runs
New average = 72 - 2 = 70 runs
1
3
2
5
1
4
80
4
7/17/2014 Alligation Rule | Aptitude Questions with Answers and Explanations
http://www.campusgate.co.in/2011/10/alligation-rule.html 5/5
Ratio of inning played (before and after) = 50 : 2 = 25 : 1
Given, innings played (after) = 4
Therefore, Inning played (before) = 25 x 4 = 100
Therefore, Total inning played = 100 + 4 = 104
Alternative Method:
Average runs in the last 4 inning = = 20 runs
Short from previous average = 72 - 20 = 52
Short (total) = 52 x 4
But, short runs (per inning) = 2 runs
Therefore, Total inning played = = 104 inning
80
4
52 × 4
2
The text passage contains a series of practice problems related to the alligation rule, each with a question and an answer provided.
multiple_questions_with_answers
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
You are on page 1of 5

# 7/17/2014 Alligation Rule | Aptitude Questions with Answers and Explanations

http://www.campusgate.co.in/2011/10/alligation-rule.html 1/5
Alligation rule helps us to find, in what ratio two mixtures with different concentrations are to be mixed to
get a target concentration.
Assume that in an engineering college ECE branch average aggregte is 80% and that of CSE is 68%. In
what ratio the students in these classes are to be mixed to get an aggregate of 76%?
Take ECE class average as , CSE class average as . If there are students in ECE and students
in CSE then the overall average is calculated as follows
If we re arrange this equation
To apply this rule easily we follow a small diagram
Eventhough alligation rule is widely applied in mixtures, we can see this rule in many areas across arithmetic
Practice Problems
1. A person covers 800km partly at a speed of 50kmph and partly at a speed of 150kmph, in 10 hours over
all. What is the distance covered at the speeds of 150 kmph?
His average speed for the entire journey is
Now we need to find in what ratio he needs to travel 800km, partly at 50kmph, and 150kmph to get
average speed of 80kmph
lligation Rule
A
1
A
2
n
1
n
2
A
avg
=
× + × n
1
A
1
n
2
A
2
+ n
1
n
2
A
avg
× + × = × ( + ) n
1
A
1
n
2
A
2
A
avg
n
1
n
2
× ( − ) = × ( − ) n
2
A
2
A
avg
n
1
A
avg
A
1
=
n
1
n
2
( − ) A
2
A
avg
( − ) A
avg
A
1
= 80
800
10
7/17/2014 Alligation Rule | Aptitude Questions with Answers and Explanations
http://www.campusgate.co.in/2011/10/alligation-rule.html 2/5
So for every 70 parts of the time travelled at 50kmph, he has to travel 30 parts are 150kmph.
As the total time is 10 hours he must have travelled = 10 hours at 150 kmph
2. The cost of oil is Rs.100 per kilogram. After adulteration with another oil, which costs Rs.50 per kilogram,
Ram sells the mixture at Rs.96 per kilogram making a profit of 20%. In what rati does he mix the two kinds
of oil?
Before applying the alligation rule we need to make sure that all the perameters are in the same units.
Here 2 costs prices and 1 selling price was given. So we should conver the selling price into cost price.
Given

Now we apply the alligation rule.
So These two must be mixed in the ratio 3:2.
3. Two solutions of milk and water are combined in the ratio 2:3 by volume. The resultant solution is a
40% milk solution. Find the milk concentration in the first solution if the concentration of milk in the second
is 60%?
It was given that are in the ratio 2:3 and second solution concentration is 60 and resultant
solution concentration is 40.
× 30
30
70 + 30
C. P × (100 + 20)% = 96
⇒C. P =
96
120%
⇒C. P = ⇒96 × = 80
96
120
100
100
120
: n
1
n
2
7/17/2014 Alligation Rule | Aptitude Questions with Answers and Explanations
http://www.campusgate.co.in/2011/10/alligation-rule.html 3/5
From the above we know that 20, 40 - x must be in the ratio 2: 3
4. A shopkeeper sold 45 kg.of goods. If he sells some quantity at a loss of 3% and rest at 17% profit,
making 5% profit on the whole, find the quantity sold at profit.
Note: 17 - 5 = 12, and 5 - (-3) = 5 + 3 = 8
Therefore, Ratio of quantities sold at profit and at loss = 8 : 12 = 2 : 3
Therefore, Quantity sold at profit = x 45 = 18 kg.
5. A mixture of 70 litres of wine and water contains 10% water. How much water should be added to make
25% water in the resulting mixture?
Therefore, The ratio is 75 : 15 = 5 : 1.
Therefore, For every 5 litres of mixture, 1 litre of water is added.
Therefore, For 70 litres, water to be added = x 70 = 14 litres.
Alternative Method:
Water = 10% of 70 litres = 7 litres
⇒ = ⇒x = 10
20
40 − x
2
3
2
5
1
5
7/17/2014 Alligation Rule | Aptitude Questions with Answers and Explanations
http://www.campusgate.co.in/2011/10/alligation-rule.html 4/5
Wine = 70 - 7 = 63 litres
Now, in the new mixture, water is 25% and wine is 75%.
Hence, in new mixture wine is 3 times of water.
Therefore, Water in new mixture = x 63 = 21 litres
Therefore, Water to be added = 21 - 7 = 14 litres
6. A man purchased a horse and a cow for Rs. 5000. He sells the horse at 20% profit and the cow at 10%
loss. If he gains 2% on the whole transaction, the cost of the horse is:
Therefore, Ratio between cost of a horse and that of a cow = 12 : 18 = 2 : 3.
Therefore, Cost of the horse = x 5000 = Rs. 2000
7. In an examination, a student gets 3 marks for every correct answer and loses 1 mark for every wrong
answer. If he scores '0' marks in a paper of 100 questions, how many of his answers were correct?
Therefore, Ratio of correct and wrong answers = 1 : 3
Therefore, Correct answers = x 100 = 25
8. The batting average of a cricket player is 72 runs per inning. In the next 4 inning, he could score only 80
runs and thereby decreases his batting average by 2 runs. What is total number of inning played by him till
last match?
Average of last 4 inning = = 20 runs
Average of inning played earlier = 72 runs
New average = 72 - 2 = 70 runs
1
3
2
5
1
4
80
4
7/17/2014 Alligation Rule | Aptitude Questions with Answers and Explanations
http://www.campusgate.co.in/2011/10/alligation-rule.html 5/5
Ratio of inning played (before and after) = 50 : 2 = 25 : 1
Given, innings played (after) = 4
Therefore, Inning played (before) = 25 x 4 = 100
Therefore, Total inning played = 100 + 4 = 104
Alternative Method:
Average runs in the last 4 inning = = 20 runs
Short from previous average = 72 - 20 = 52
Short (total) = 52 x 4
But, short runs (per inning) = 2 runs
Therefore, Total inning played = = 104 inning
80
4
52 × 4
2
user
The text passage contains a series of practice problems related to the alligation rule, each with a question and an answer provided.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS