To Make a Mixture from Two Mixtures MCQ Quiz - Objective Question with Answer for To Make a Mixture from Two Mixtures - Download Free PDF

Last updated on Jun 11, 2025

To Make a Mixture from Two Mixtures is an essential sub-topic of Ratio and proportion, which is a topic of Mathematics. Make a Mixture from Two Mixtures questions hold quite a weightage in distinct government examinations and is known for testing the aspirants’ aptitude. Testbook presents Make a Mixture from Two Mixtures MCQs Quiz to help you in analysing your preparation for this section. Nevertheless, to assist you, even more, solutions to all the questions and explanations for the same are also stated.

Latest To Make a Mixture from Two Mixtures MCQ Objective Questions

To Make a Mixture from Two Mixtures Question 1:

A vessel contains 108 litres of milk and water in the ratio of 5:4. If 20 Liters of milk and 36 liter water is added to the mixture then difference between milk and water in mixture ix Y. Find the value of 7Y?

  1. 40
  2. 28
  3. 32
  4. 44
  5. 42

Answer (Detailed Solution Below)

Option 2 : 28

To Make a Mixture from Two Mixtures Question 1 Detailed Solution

Given:

Total volume of mixture = 108 liters

Ratio of milk to water = 5:4

Milk added = 20 liters

Water added = 36 liters

Formula used:

Milk in the mixture = (Total mixture) × (Ratio of milk / Total ratio)

Water in the mixture = (Total mixture) × (Ratio of water / Total ratio)

Calculations:

Total ratio of milk and water = 5 + 4 = 9

Milk in the mixture = (108 liters) × (5/9) = 60 liters

Water in the mixture = (108 liters) × (4/9) = 48 liters

After adding milk and water:

New amount of milk = 60 + 20 = 80 liters

New amount of water = 48 + 36 = 84 liters

Difference between milk and water in the mixture = 84 - 80 = 4 liters

Y = 4

7Y = 7 × 4 = 28

∴ The value of 7Y is 28.

To Make a Mixture from Two Mixtures Question 2:

Can A and Can B contain a mixture of soda and water in the ratio of 5 : 3 and 7 : 2 respectively If soda and water are taken out in the ratio of P : Q from can A and B respectively to form a new mixture in which the ratio of soda and water is 12 : 5 respectively, then find the value Of P:Q?

  1. 6 : 5
  2. 8 : 9
  3. 5 : 4
  4. 4 : 3
  5. 3 : 2

Answer (Detailed Solution Below)

Option 2 : 8 : 9

To Make a Mixture from Two Mixtures Question 2 Detailed Solution

​Calculations:

Let the amount of mixture taken out from Can A be x units, and the amount taken from Can B be y units.

In Can A, the ratio of soda to water is 5:3. So, the amount of soda taken out from Can A is:

Soda taken from Can A = (5/8) × x, and water taken from Can A = (3/8) × x.

In Can B, the ratio of soda to water is 7 : 2. So, the amount of soda taken out from Can B is:

Soda taken from Can B = (7/9) × y, and water taken from Can B = (2/9) × y.

Now, the total amount of soda and water in the new mixture must have a ratio of 12 : 5.

The total amount of soda in the new mixture = (5/8) × x + (7/9) × y.

The total amount of water in the new mixture = (3/8) × x + (2/9) × y.

The ratio of soda to water in the new mixture is 12 : 5. So, we can write:

\(\dfrac{(5/8) \times x + (7/9) \times y}{(3/8) \times x + (2/9) \times y} = \dfrac{12}{5}\)

Cross-multiply:

(5/8) × x + (7/9) × y = (12/5) × ((3/8) × x + (2/9) × y)

Now, simplifying this equation, we multiply through by 40 (LCM of 8, 9, and 5):

40 × [(5/8) × x + (7/9) × y] = 40 × (12/5) × [(3/8) × x + (2/9) × y]

After simplification, solving this will give the ratio of P : Q.

Therefore, after solving the equation, you will get P : Q = 8 : 9.

To Make a Mixture from Two Mixtures Question 3:

Two vessels containing 31 litres and 43 litres quantity of solution, have milk and water in the ratio of 15:16 and 26:17 respectively. If the solutions are mixed with each other, then how many litres of water has to be added in the final solution to make the resulting solution in the ratio 1:1?

  1. 12
  2. 6
  3. 10
  4. 8

Answer (Detailed Solution Below)

Option 4 : 8

To Make a Mixture from Two Mixtures Question 3 Detailed Solution

Given:

Vessel 1: 31 litres, Milk : Water = 15 : 16

Vessel 2: 43 litres, Milk : Water = 26 : 17

Required: Add water to make final Milk : Water = 1 : 1

Formula used:

Milk = Total Quantity × (Milk Ratio / Total Ratio)

Water = Total Quantity × (Water Ratio / Total Ratio)

Calculations:

Milk in Vessel 1 = 31 × 15 / (15 + 16) = 31 × 15 / 31 = 15 L

Water in Vessel 1 = 31 - 15 = 16 L

Milk in Vessel 2 = 43 × 26 / (26 + 17) = 43 × 26 / 43 = 26 L

Water in Vessel 2 = 43 - 26 = 17 L

Total Milk = 15 + 26 = 41 L

Total Water = 16 + 17 = 33 L

Required: Milk = Water ⇒ 41 = 33 + x

⇒ x = 8 L

∴ Water to be added = 8 litres

To Make a Mixture from Two Mixtures Question 4:

A mixture containing three immiscible liquids — A, B, and C — has liquids A and B in the ratio 1 : 2, and the quantity of liquid C is 20 litres. When 5 litres of liquid C and 2 litres of liquid A are removed and replaced by an equal amount of liquid B, the new ratio of A to B becomes 1 : 3. What is the total volume of the mixture in litres?

Answer (Detailed Solution Below) 59

To Make a Mixture from Two Mixtures Question 4 Detailed Solution

Explanation:

Let the initial volume of liquids A and B be x and 2x.

Total volume of mixture = x + 2x + 20 = 3x + 20

Final volume of liquid A = x − 2

Final volume of liquid B = 2x + 7

Final volume of liquid C = 15

Therefore, 3(x-2)=(2x+7).

x = 13.

Volume of the mixture = 3x + 20 = 59 litres.

To Make a Mixture from Two Mixtures Question 5:

In what ratio must a grocer mix two varieties of pulses costing Rs.75 and Rs.100 per kg respectively so as to get a mixture worth Rs.86.5 per kg? (In kg)

  1. 21:23
  2. 23:25
  3. 25:27
  4. 27:23

Answer (Detailed Solution Below)

Option 4 : 27:23

To Make a Mixture from Two Mixtures Question 5 Detailed Solution

Given:

Cost of the first variety of pulses = Rs. 75 per kg

Cost of the second variety of pulses = Rs. 100 per kg

Cost of the mixture = Rs. 86.5 per kg

Formula Used:

Ratio of quantities = (Cost of second variety - Cost of mixture) : (Cost of mixture - Cost of first variety)

Calculation:

Let the ratio be x : y.

Cost of second variety - Cost of mixture = 100 - 86.5 = 13.5

Cost of mixture - Cost of first variety = 86.5 - 75 = 11.5

Ratio of quantities = 13.5 : 11.5

⇒ Ratio = 135 : 115

⇒ Ratio = 27 : 23

The grocer must mix the pulses in the ratio 27:23.

Top To Make a Mixture from Two Mixtures MCQ Objective Questions

In a vessel, a mixture of milk and water is in ratio 8 : 7, while in another vessel mixture of milk and water is in ratio 7 : 9. In what ratio mixture of both the vessels should be mixed together so that in the resultant mixture ratio of water and milk becomes 9 : 8?

  1. 135 : 256
  2. 256 : 135
  3. 265 : 129
  4. 129 : 265

Answer (Detailed Solution Below)

Option 1 : 135 : 256

To Make a Mixture from Two Mixtures Question 6 Detailed Solution

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Given:

The ratio of milk and water in the first vessel = 8 : 7

The ratio of milk and water in the second vessel = 7 : 9

The ratio of water and milk in the resultant mixture = 9 : 8

Calculation:

Let x litre of the first mixture and y litre of the second mixture are mixed.

Quantity of milk in x litre of the first mixture = 8x/15

Quantity of milk in y litre of the second mixture = 7y/16

Total quantity of the resultant mixture = (x + y)

Quantity of milk in (x + y) litre of the resultant mixture = 8(x + y)/17

8x/15 + 7y/16 = 8(x + y)/17

⇒ 8x/15 + 7y/16 = 8x/17 + 8y/17

⇒ 8x/15 – 8x/17 = 8y/17 – 7y/16

⇒ (136x – 120x)/15 × 17 = (128y – 119y)/17 × 16

⇒ 16x/15 = 9y/16

⇒ 256x = 135y

⇒ x/y = 135/256

 The required ratio is 135 : 256

Alternative Method:

The concentration of milk in the first mixture = 8/15

The concentration of milk in the second mixture = 7/16

The concentration of milk in the resultant mixture = 8/17

By the rule of Allegation,

F1 Ashish 4.12.20 Pallavi D11

⇒ 9/272 : 16/255

⇒ 9 × 255 : 16 × 272

⇒ 9 × 15 : 16 × 16

⇒ 135 : 256     

 The required ratio is 135 : 256.

A dairy farmer's can contains 6 litres of milk. His wife adds some water to it such that milk and water are in the ratio 4 ∶ 1. How many litres of milk should the farmer add so that the milk and water are in the ratio 5 ∶ 1?

  1. 1.5
  2. 1.2
  3. 1.0
  4. 1.8

Answer (Detailed Solution Below)

Option 1 : 1.5

To Make a Mixture from Two Mixtures Question 7 Detailed Solution

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Given:

A dairy farmer's can contains 6 litres of milk.

His wife adds some water to it such that milk and water are in the ratio 4 ∶ 1.

Calculation:

Milk : Water = 4 : 1

Let the quantity of milk and water be 4x and x.

Quantity of Milk = 4x = 6 litres

⇒ x = 1.5 litres

Quantity of Water = x = 1.5 litres

According to the question,

\(\dfrac{6+x}{1.5}\) = \(\dfrac{5}{1}\)

⇒ 6 + x = 7.5

⇒ x = 7.5 - 6 = 1.5 litres

Alternate Method qImage67389354af6c9065c1064f57

The ratio of sugar to water in solution A is 1  4 and the ratio of salt to water in solution B is 1 26. To make an ORS solution, A and B are mixed in 2 3. Find the ratio of sugar to salt in ORS.

  1. 45 ∶ 16
  2. 52 15 
  3. 18 5
  4. 12 7

Answer (Detailed Solution Below)

Option 3 : 18 5

To Make a Mixture from Two Mixtures Question 8 Detailed Solution

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Given:

The ratio of sugar to water in solution A = 1  4

The ratio of salt to water in solution B = 1  26

Calculation:

First, make the quantity of solution A and solution B same.

Total unit of sugar and water in solution A = 1 + 4 = 5 units

Total unit of salt and water in solution B = 1 + 26 = 27 units

Now, multiply the ratio of solution A by 27 and multiply the ratio of solution B by 5.

The ratio of sugar to water in solution A = 1 × 27 ∶ 4 × 27 = 27 : 108

The ratio of salt to water in solution B = 1 × 5 ∶ 26 × 5 = 5 : 130

Now, mix the solution 2 : 3.

Therefore, multiply the new ratio of solution A by 2 and multiply the new ratio of the solution B by 3.

The new required ratio of solution A = 54 : 216

The new required ratio of solution B = 15 : 390

The ratio of sugar, salt and water in ORS = 54 : 15 : 606

The ratio of sugar and salt = 54 : 15 = 18 : 5

Therefore, "18 : 5" is the required answer.

Shortcut Trick qImage67c061c6956a617c7b9c4771

In what ratio should water be mixed with wine, that costs Rs. 60 per liter, so that the price of the resultant mixture is Rs.40 per litre?

  1. 2 ∶ 3
  2. 3 ∶ 4
  3. 1 ∶ 2
  4. 4 ∶ 5

Answer (Detailed Solution Below)

Option 3 : 1 ∶ 2

To Make a Mixture from Two Mixtures Question 9 Detailed Solution

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Given: 

The cost price of wine = Rs. 60 per litre

The cost price of water = Rs. 0 per litre

The cost price of mixture = Rs. 40 per litre

Calculations:

Let the quantity of wine and water added in final mixture be x and y respectively.

According to the question:

60 × x + 0y = (x + y) × 40

⇒ 60x  = 40x + 40y

⇒ 60x - 40x = 40y

⇒ 20x = 40y

⇒ x : y = 2 : 1

∴ The ratio in which water and wine should be mixed is 1 : 2.

Alternate Method

Given: 

The cost price of wine = Rs. 60 per litre

The cost price of water = Rs. 0 per litre

The cost price of mixture = Rs. 40 per litre

Concept used:

If two indigents are mixed, then

Calculation:

Using alligation, 

F2 Suhani Kumari 20-5-2021 Swati D1

Ratio of wine and water = 40 : 20 = 2 :1

∴ The ratio in which water and wine should be mixed is 1 : 2.

Important Points

 

F2 Suhani Kumari 20-5-2021 Swati D2

If two qualities of pulses ‘X’ and ‘Y’ of prices Rs. 100 and Rs. 150 per kg are mixed in the ratio 7 ∶ 20, then what is the price (in Rs.) of this mixture of pulses (correct to the nearest Rupee)? 

  1. 137
  2. 135
  3. 134
  4. 136

Answer (Detailed Solution Below)

Option 1 : 137

To Make a Mixture from Two Mixtures Question 10 Detailed Solution

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Given:

Price of X qualities of pulses = Rs.100/kg

Price of Y qualities of pulses = Rs.150/kg

Qunatity of X type of pulses : Qunatity of Y type of pulses = 7 : 20

Formula used:

Average price = (Total price of mixture of two quality of grain)/Total quantity

Calculation:

Let quantity of X type of pulses = 7x

Quantity of X type of pulses = 20x

Average price = (Total price of mixture of two quality of grain)/Total quantity

⇒ {(100 × 7x) + (150 × 20x)}/27x

⇒ (700x + 3000x)/27x

⇒ 3700x/27x = Rs.137.03 ≈ Rs.137

∴ The correct answer is Rs.137.

Shortcut Trick F2 State G Arbaz 5-3-24 D1

\(\frac{150-m}{m-100}= \frac{7}{20}\)

⇒ 3000 - 20m = 7m - 700

⇒ 3700 = 27m

⇒ m = 3700/27 

 ⇒ m =Rs.137.03 ≈ Rs.137

∴ The correct answer is Rs.137.

80 litres of a mixture contains milk and water in the ratio of 27 ∶ 5. How much more water is to be added to get a mixture containing milk and water in the ratio of 3 ∶ 1?

  1. 10 litres
  2. 15 litres
  3. 20 litres
  4. 25 litres

Answer (Detailed Solution Below)

Option 1 : 10 litres

To Make a Mixture from Two Mixtures Question 11 Detailed Solution

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Given:

80 liters of a mixture contain milk and water in the ratio of 27 ∶ 5.

Calculation:

Milk = \(\dfrac{27}{32}\) × 80 = 67.5 L

Water = 80 - 67.5 = 12.5 L

Let, m = water to be added to get 3 : 1

\(\dfrac{67.5}{12.5 + m}\) = 3

⇒ 67.5 = 37.5 + 3m

⇒ m = 10

∴ The quantity of water to be added to get 3 : 1, is 10 litres.

Two vessels A and B contain spirit and water in the ratio 3 : 8 and 6 : 5. In what ratio should their ingredients be mixed to obtain a solution of spirit and water in the ratio 5 : 6?

  1. 1 : 2
  2. 6 : 7
  3. 2 : 3
  4. 4 : 5

Answer (Detailed Solution Below)

Option 1 : 1 : 2

To Make a Mixture from Two Mixtures Question 12 Detailed Solution

Download Solution PDF

Given:

A and B contain spirit and water in the ratio 3 : 8 and 6 : 5 respectively

Calculation:

F1 Madhuri Defence 29.08.2022 D1

∴ Required ratio = (1/11) : (2/11) = 1 : 2

Alternate Method

Let the total quantity in A be 11x and in B be 11y, which is to be mixed

According to the question:

(3x + 6y)/(8x + 5y) = 5/6

⇒ 18x + 36y = 40x + 25y

⇒ 22x = 11y

⇒ x/y = 1/2

∴ They should be mixed in the ratio 1 : 2

2/3 of a milk-water mixture was milk. There was 21 litres of the mixture. If 4 litres of water is added to it, Then find the percentage of milk in the new mixture.

  1. 44
  2. 56
  3. 14
  4. 11

Answer (Detailed Solution Below)

Option 2 : 56

To Make a Mixture from Two Mixtures Question 13 Detailed Solution

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Total volume = 21 litres

2/3 of a milk-water mixture was milk,

⇒ Volume of milk = 2/3 × 21 = 14 litres

⇒ Volume of water = 21 – 14 = 7 litres

4 litres of water is added to it,

⇒ New volume of water = 7 + 4 = 11 litres.

⇒ Total volume of mixture = 14 + 11 = 25

∴ Percentage of milk = 14/25 × 100 = 56%

Milk and water in a solution of 56 ml is such that after replacing 16 ml of the solution and adding 5 ml of water, the milk and water ratio is 5 ∶ 4. What was the concentration of milk in the mixture initially?

  1. 38 ml
  2. 35 ml
  3. 21 ml
  4. 28 ml

Answer (Detailed Solution Below)

Option 2 : 35 ml

To Make a Mixture from Two Mixtures Question 14 Detailed Solution

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Let the quantity of milk and water in the mixture be x and 56 – x

Now, 16ml of the solution is is removed

Quantity of solution replaced will be removed in the same ratio as the contents in the solution

∴ Quantity of milk left after removal = x – (16 × x/56) = 5x/7

Quantity of water left after removal = 56 – x – {16 × (56 – x)/56} = 40 – 5x/7

Ratio of milk and water after adding 5 ml of water is 5 ∶ 4

⇒ (5x/7)/(40 + 5 – 5x/7) = 5/4

⇒ 20x = 45 × 7 × 5 – 25x

⇒ x = 7 × 5 = 35

∴ Concentration of milk in the mixture initially was 35 ml

Alternate Method

Quantity of Solution = 56 ml (Given)

16 ml of the solution replaced with 5 ml of water

then the solution quantity will be = (56 – 16) + 5 = 45 ml

Milk : Water = 5 : 4

M + W = 45 (will have to be distributed in the ratio of 5 : 4) 

In the Final Mixture,

Milk = 25 ml, Water = 20 ml

In 20 ml Water, 5 litre was added after replacement.

∴ Before Replacement, Water = 20 - 5 = 15 ml

Ratio of Milk and Water (Initially) = 25 : 15 = 5 : 3

16 ml of solution was replaced (will be calculated in the ratio of 5 : 3)

Replaced Quantity of Milk and Water = 10 ml and 6 ml  

Hence, Initial Quantity of Milk = 25 ml + 10 ml = 35 ml

A bartender makes a mixture of 18 litres of wine and soda, it contains 30% soda. How much soda should be added to it to increase the percentage of soda to 40%?

  1. 3
  2. 2
  3. 4
  4. 3.5

Answer (Detailed Solution Below)

Option 1 : 3

To Make a Mixture from Two Mixtures Question 15 Detailed Solution

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Given:

Quantity of mixture is 18 litres

Percentage of soda is 30%

Percentage of wine is 70%

Calculation:

Quantity of soda = 30% of 18 = 5.4 litres

Quantity of wine = 70% of 18 = 12.6 litres

Let the quantity of soda added be x

Total quantity = 18 + x

According to the question

(5.4 + x)/(18 + x) = 40/100

⇒ (5.4 + x)/(18 + x) = 2/5

⇒ 27 + 5x = 36 + 2x

⇒ x = 3 litres

∴ The required quantity of soda is 3 litres.

Shortcut Trick

 F1 Piyush Madhuri 02.06.2021 D2

Ratio = 6 : 1

⇒ 6 = 18 litres

⇒ 1 = 3 litres 

∴ The required quantity of soda is 3 litres.

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