Aptitude
Mixture and Alligation

Mixture and Alligation Question answer : Aptitude Test – 1

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Sep 2, 2016

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Last Updated on Mar 15, 2023

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Quiz Description :

Name: Mixture and Alligation Question answer : Aptitude Test – 1

Subject: Aptitude

Topic: Mixture and Alligation

Questions: 10 Objective Type

Time Allowed: 15 minutes

Important for: IBPS PO, IBPS Clerk, SBI PO, SBI Clerk, RBI, LIC AAO, SSC CGL, SSC CHSL, State Police, Indian Army, CRPF, State PCS, Engineering Job Interview etc.

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Question 1 of 10

1. Question
1 points
In what proportion must rice at Rs. 3.10 per kg be mixed with rice at Rs. 3.60 per kg, so that the mixture be worth Rs. 3.25 a kg?
- 3 : 7
- 7: 3
- 7 : 5
- 3 : 5
Correct

C.P of 1 Kg. cheaper rice C.P of 1 Kg. dearer rice

310 Paise 360 Paise

Mean Price
(325 Paise)

35 15

By applying Alligation rule:

(Quality of cheaper Rice)/(Quality of dearer Rice)= 35/15= 7/3

Hence they must be mixed in the ratio 7 : 3.

Incorrect

C.P of 1 Kg. cheaper rice C.P of 1 Kg. dearer rice

310 Paise 360 Paise

Mean Price
(325 Paise)

35 15

By applying Alligation rule:

(Quality of cheaper Rice)/(Quality of dearer Rice)= 35/15= 7/3

Hence they must be mixed in the ratio 7 : 3.

Unattempted

C.P of 1 Kg. cheaper rice C.P of 1 Kg. dearer rice

310 Paise 360 Paise

Mean Price
(325 Paise)

35 15

By applying Alligation rule:

(Quality of cheaper Rice)/(Quality of dearer Rice)= 35/15= 7/3

Hence they must be mixed in the ratio 7 : 3.
Question 2 of 10

2. Question
1 points
What amount of salt at ₹56 per Kg. must a salesman mix with ₹36 Kg. of salt at ₹28 per Kg. so that salesman may, on selling the mixture at ₹48 per Kg., gain 20% on the outlay?
- 29 Kg
- 36 Kg
- 27 Kg
- 25 Kg
Correct

The cost price of mixture = 48 × 100/120 P=₹40 per Kg                                (By the rule of fraction)

56 28

40

12 16

3 4

∴ Ratio = 3 : 4
Thus for every 4 Kg. of salt at ₹28, 3 Kg. of salt at ₹56 is used.
∴ The required no. of Kg. = 36 × 3/4 = 27 Kg

Incorrect

The cost price of mixture = 48 × 100/120 P=₹40 per Kg                                (By the rule of fraction)

56 28

40

12 16

3 4

∴ Ratio = 3 : 4
Thus for every 4 Kg. of salt at ₹28, 3 Kg. of salt at ₹56 is used.
∴ The required no. of Kg. = 36 × 3/4 = 27 Kg

Unattempted

The cost price of mixture = 48 × 100/120 P=₹40 per Kg                                (By the rule of fraction)

56 28

40

12 16

3 4

∴ Ratio = 3 : 4
Thus for every 4 Kg. of salt at ₹28, 3 Kg. of salt at ₹56 is used.
∴ The required no. of Kg. = 36 × 3/4 = 27 Kg
Question 3 of 10

3. Question
1 points
A milkman mixes of a certain quantity of milk with 16 liters of water is worth 90 P per liter. If pure milk be worth Rs. 1.08 per liter how much milk is there in the mixture?
- 100 litres
- 80 ml
- 80 Litres
- 90 litres
Correct

The mean value is 90 P and the price of water is 0 P.

Milk Water

108 0

90

90 18

By Applying Alligation Rule;
Milk and Water are in the ratio of 5 : 1.
∴ Quantity of milk in the mixture = 5 × 16 = 80 litres

Incorrect

The mean value is 90 P and the price of water is 0 P.

Milk Water

108 0

90

90 18

By Applying Alligation Rule;
Milk and Water are in the ratio of 5 : 1.
∴ Quantity of milk in the mixture = 5 × 16 = 80 litres

Unattempted

The mean value is 90 P and the price of water is 0 P.

Milk Water

108 0

90

90 18

By Applying Alligation Rule;
Milk and Water are in the ratio of 5 : 1.
∴ Quantity of milk in the mixture = 5 × 16 = 80 litres
Question 4 of 10

4. Question
1 points
A butler stole wine from a butt of sherry which contained 40% of spirit. He replaced what he had stolen by wine containing only 16% spirit. The butt was then of 24% strength only. How much of the butt did he steal?
- 3/2
- 1/2
- 1/4
- 2/3
Correct

Explanation:

Wine Containing Wine Containing

40% Spirit 16% Spirit

Water Containing
(24% Spirit)

8 16

∴ By allegation rule:

(Wine with 40% spirit)/(Wine with 16% spirit)= 8/16= 1/2
i.e., they must be mixed in the ratio (1 : 2). Thus 1/3 of the butt of sherry was left and hence the butler drew out 2/3 of the butt.

Incorrect

Explanation:

Wine Containing Wine Containing

40% Spirit 16% Spirit

Water Containing
(24% Spirit)

8 16

∴ By allegation rule:

(Wine with 40% spirit)/(Wine with 16% spirit)= 8/16= 1/2
i.e., they must be mixed in the ratio (1 : 2). Thus 1/3 of the butt of sherry was left and hence the butler drew out 2/3 of the butt.

Unattempted

Explanation:

Wine Containing Wine Containing

40% Spirit 16% Spirit

Water Containing
(24% Spirit)

8 16

∴ By allegation rule:

(Wine with 40% spirit)/(Wine with 16% spirit)= 8/16= 1/2
i.e., they must be mixed in the ratio (1 : 2). Thus 1/3 of the butt of sherry was left and hence the butler drew out 2/3 of the butt.
Question 5 of 10

5. Question
1 points
In what proportion may three kinds of wheat at Rs. 1.27, Rs. 1.29 and Rs. 1.32 per Kg. be mixed to produce mixture worth Rs. 1.30 per Kg?
- 2 : 2 : 3
- 1 : 1 : 2
- 2 : 1 : 2
- 1 : 2 : 2
Correct

Explanation:

Method 1:

1^st Wheat 2^nd Wheat 3^rd Wheat Mean Price

127 P 129 P 132 P 130 P

Here the first two prices are less and the third price is greater than the mean price.
We first find the proportion in which wheat at 127 P and 132 P must be mixed to produce a mixture at 130 P.
(i)

1^st Wheat 3^rd Wheat

127 132

130

2 3

The proportion is 2 : 3.
We next find the proportion in which wheat at 129 P and 132 P must be mixed to produce a mixture at 130 P.

2^nd Wheat 3^rd Wheat

129 132

130

2 1

The proportion is 2 : 1.

∴ The required proportion is = 2 : 2 : 4 = 1 : 1 : 2

Incorrect

Explanation:

Method 1:

1^st Wheat 2^nd Wheat 3^rd Wheat Mean Price

127 P 129 P 132 P 130 P

Here the first two prices are less and the third price is greater than the mean price.
We first find the proportion in which wheat at 127 P and 132 P must be mixed to produce a mixture at 130 P.
(i)

1^st Wheat 3^rd Wheat

127 132

130

2 3

The proportion is 2 : 3.
We next find the proportion in which wheat at 129 P and 132 P must be mixed to produce a mixture at 130 P.

2^nd Wheat 3^rd Wheat

129 132

130

2 1

The proportion is 2 : 1.

∴ The required proportion is = 2 : 2 : 4 = 1 : 1 : 2

Unattempted

Explanation:

Method 1:

1^st Wheat 2^nd Wheat 3^rd Wheat Mean Price

127 P 129 P 132 P 130 P

Here the first two prices are less and the third price is greater than the mean price.
We first find the proportion in which wheat at 127 P and 132 P must be mixed to produce a mixture at 130 P.
(i)

1^st Wheat 3^rd Wheat

127 132

130

2 3

The proportion is 2 : 3.
We next find the proportion in which wheat at 129 P and 132 P must be mixed to produce a mixture at 130 P.

2^nd Wheat 3^rd Wheat

129 132

130

2 1

The proportion is 2 : 1.

∴ The required proportion is = 2 : 2 : 4 = 1 : 1 : 2
Question 6 of 10

6. Question
1 points
Milk and water are mixed in a vessel A in the proportion 5 : 2, and in vessel B in the proportion 8 : 5. In what proportion should quantities be taken from the two vessels so as to from a mixture in which milk and water will be in the proportion of 9 : 4?
- 2 : 7
- 9 : 7
- 2 : 5
- 7 : 2
Correct

Explanation:

In vessel A, milk = 5/7 of the weight of mixture
In vessel B, milk = 8/13 of the weight of mixture. Now we want to from a mixture in which milk will be 9/13 of the weight of this mixture.

Applying allegation rule:

5/7 8/13

9/13

1/13 2/91

∴ Required proportion is = 1/13 : 2/91 = 7 : 2

Incorrect

Explanation:

In vessel A, milk = 5/7 of the weight of mixture
In vessel B, milk = 8/13 of the weight of mixture. Now we want to from a mixture in which milk will be 9/13 of the weight of this mixture.

Applying allegation rule:

5/7 8/13

9/13

1/13 2/91

∴ Required proportion is = 1/13 : 2/91 = 7 : 2

Unattempted

Explanation:

In vessel A, milk = 5/7 of the weight of mixture
In vessel B, milk = 8/13 of the weight of mixture. Now we want to from a mixture in which milk will be 9/13 of the weight of this mixture.

Applying allegation rule:

5/7 8/13

9/13

1/13 2/91

∴ Required proportion is = 1/13 : 2/91 = 7 : 2
Question 7 of 10

7. Question
1 points
300 gm of sugar solution has 40% sugar in it. How much sugar should be added to make it 50% in the solution?
- 100 gms
- 90 gms
- 60 gms
- 50 gms
Correct

Method 1:

The existing solution has 40% sugar. And sugar is to mixed; so the other solution has 100% sugar. So by allegation method:

40% 100%

50%

50% 10%

∴ The ratio mixture should be added in the ratio 5 : 1.
Therefore, required sugar = 300/5 ×1 = 60 gms.

Method 2:

Quantity of sugar added = (Solution (Required % value – Present % value))/((100-required % value)) = ([300 ×(50 – 40)])/((100 – 50) ) = 60 gms.

Incorrect

Method 1:

The existing solution has 40% sugar. And sugar is to mixed; so the other solution has 100% sugar. So by allegation method:

40% 100%

50%

50% 10%

∴ The ratio mixture should be added in the ratio 5 : 1.
Therefore, required sugar = 300/5 ×1 = 60 gms.

Method 2:

Quantity of sugar added = (Solution (Required % value – Present % value))/((100-required % value)) = ([300 ×(50 – 40)])/((100 – 50) ) = 60 gms.

Unattempted

Method 1:

The existing solution has 40% sugar. And sugar is to mixed; so the other solution has 100% sugar. So by allegation method:

40% 100%

50%

50% 10%

∴ The ratio mixture should be added in the ratio 5 : 1.
Therefore, required sugar = 300/5 ×1 = 60 gms.

Method 2:

Quantity of sugar added = (Solution (Required % value – Present % value))/((100-required % value)) = ([300 ×(50 – 40)])/((100 – 50) ) = 60 gms.
Question 8 of 10

8. Question
1 points
A person travels 285 Km in 6 hrs in two stages. In the first part of the journey, he travels by bus at the speed of 40 Km per hr. In the second part of the journey, he travels by train at the speed of 55 km per hr. How much distance did he travel by train?
- 150 km
- 148.2 km
- 142.5 km
- 190.8 km
Correct

Explanation:

By applying the allegation method on the speed.

Speed of Bus Speed of Train

40 55

Average Speed
285/6

45/6 45/6

∴ Time spent in bus : Time spent in train = 45/6 : 45/6 = 1 : 1
∴ Distance travelled by Train = 285/2 = 142.5 km.

Incorrect

Explanation:

By applying the allegation method on the speed.

Speed of Bus Speed of Train

40 55

Average Speed
285/6

45/6 45/6

∴ Time spent in bus : Time spent in train = 45/6 : 45/6 = 1 : 1
∴ Distance travelled by Train = 285/2 = 142.5 km.

Unattempted

Explanation:

By applying the allegation method on the speed.

Speed of Bus Speed of Train

40 55

Average Speed
285/6

45/6 45/6

∴ Time spent in bus : Time spent in train = 45/6 : 45/6 = 1 : 1
∴ Distance travelled by Train = 285/2 = 142.5 km.

Question 9 of 10

9. Question

1 points

Mira’s expenditure and saving are in the ratio 3 : 2. Her income increase by 10%. Her expenditure also increase by 12%. By how many % does her saving increase?

Correct

Explanation:

Expenditure		Saving
12		x
% Increase in Expenditure		% Increase in Saving

	10
	% Increase in income

3		2

∴ Required % increase = 7%

Incorrect

Explanation:

Expenditure		Saving
12		x
% Increase in Expenditure		% Increase in Saving

	10
	% Increase in income

3		2

∴ Required % increase = 7%

Unattempted

Explanation:

Expenditure		Saving
12		x
% Increase in Expenditure		% Increase in Saving

	10
	% Increase in income

3		2

∴ Required % increase = 7%

Question 10 of 10

10. Question
1 points
A container contained 80 Kg of milk. From this container 8 Kg of milk was taken out and replaced by water. This process was further repeated two times. How much milk is now contained by the container?
- 68.95 Kg
- 58.32 Kg
- 55.32 Kg
- 54.98 Kg
Correct

Amount of liquid left after n operation, when the container originally contains x units of liquid form which y units is taken out each time is

=x((x – y)/x)^n units
Thus, in the above case, amount of milk left = =80((80 – 8)/80)^3 Kg. = 58.32 Kg.

Incorrect

Amount of liquid left after n operation, when the container originally contains x units of liquid form which y units is taken out each time is

=x((x – y)/x)^n units
Thus, in the above case, amount of milk left = =80((80 – 8)/80)^3 Kg. = 58.32 Kg.

Unattempted

Amount of liquid left after n operation, when the container originally contains x units of liquid form which y units is taken out each time is

=x((x – y)/x)^n units
Thus, in the above case, amount of milk left = =80((80 – 8)/80)^3 Kg. = 58.32 Kg.

Also check
Aptitude test for IBPS PO / Clerk / SO
Aptitude test for Railway exams
Mixture and Alligation Aptitude question answer test
Online Quantitative Aptitude MCQ Quiz for competitive exams

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C.P of 1 Kg. cheaper rice		C.P of 1 Kg. dearer rice
310 Paise		360 Paise

	Mean Price (325 Paise)

35		15

Wine Containing		Wine Containing
40% Spirit		16% Spirit

	Water Containing (24% Spirit)

8		16

1^st Wheat	2^nd Wheat	3^rd Wheat	Mean Price
127 P	129 P	132 P	130 P

Milk		Water
108		0

	90

90		18

Milk		Water
108		0

	90

90		18

Milk		Water
108		0

	90

90		18

5/7		8/13

	9/13

1/13		2/91

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