To make a mixture from two Quantity MCQ Quiz - Objective Question with Answer for To make a mixture from two Quantity - Download Free PDF
Last updated on Jun 6, 2025
Latest To make a mixture from two Quantity MCQ Objective Questions
To make a mixture from two Quantity Question 1:
A jar contains a mixture of 2 liquids P and Q in the ratio 4:1. When 10 litres of the mixture is taken out and 10 litres of liquid Q is poured into the jar, the ratio becomes 2:3. How many litres of the liquid P was contained in the jar?
Answer (Detailed Solution Below)
To make a mixture from two Quantity Question 1 Detailed Solution
Given:
A jar contains a mixture of two liquids P and Q in the ratio 4:1.
10 litres of the mixture is taken out, and 10 litres of liquid Q is added to the jar.
The new ratio becomes 2:3.
Formula used:
Let the initial quantity of liquid P be 4x and liquid Q be x.
After removing 10 litres of the mixture:
Liquid P removed = \(\frac{4}{5} \times 10\) = 8 litres.
Liquid Q removed = \(\frac{1}{5} \times 10\) = 2 litres.
The remaining quantities after removal:
Liquid P = 4x - 8.
Liquid Q = x - 2.
Adding 10 litres of liquid Q:
New liquid Q = (x - 2) + 10.
New ratio of P:Q = 2:3.
Equation: \(\frac{\text{Liquid P}}{\text{Liquid Q}} = \frac{2}{3}\)
Calculation:
\(\frac{4x - 8}{x - 2 + 10} = \frac{2}{3}\)
⇒ \(\frac{4x - 8}{x + 8} = \frac{2}{3}\)
⇒ 3(4x - 8) = 2(x + 8)
⇒ 12x - 24 = 2x + 16
⇒ 12x - 2x = 16 + 24
⇒ 10x = 40
⇒ x = 4
Initial liquid P = 4x = 4 × 4 = 16 litres.
∴ The correct answer is option (2).
To make a mixture from two Quantity Question 2:
The ratio of two liquids B1 and B2 in a container is 3 ∶ 2. When 10 litres of mixture is removed from the container and is replaced with B2, the ratio of B1 and B2 becomes 3 ∶ 5. How many litres of B1 was in the container initially?
Answer (Detailed Solution Below)
To make a mixture from two Quantity Question 2 Detailed Solution
Given:
Initial ratio B1 : B2 = 3 : 2
Mixture removed = 10 litres
Replaced with = B2
Final ratio B1 : B2 = 3 : 5
Formula Used:
Amount of B1 removed = (Ratio of B1 / Total ratio) × Quantity removed
Amount of B2 removed = (Ratio of B2 / Total ratio) × Quantity removed
Calculations:
Let initial quantity of B1 = 3x litres
Let initial quantity of B2 = 2x litres
Amount of B1 in 10 litres removed mixture = (3 / (3 + 2)) × 10 = (3/5) × 10 = 6 litres
Amount of B2 in 10 litres removed mixture = (2 / (3 + 2)) × 10 = (2/5) × 10 = 4 litres
Remaining B1 = 3x - 6
Remaining B2 = 2x - 4
After adding 10 litres of B2, final quantity of B2 = 2x - 4 + 10 = 2x + 6
Final ratio:
⇒ (3x - 6) / (2x + 6) = 3 / 5
⇒ 5 × (3x - 6) = 3 × (2x + 6)
⇒ 15x - 30 = 6x + 18
⇒ 9x = 48
⇒ x = 48 / 9 = 16 / 3
Initial quantity of B1 = 3x = 3 × (16 / 3) = 16 litres
∴ Initially, there were 16 litres of B1 in the container.
To make a mixture from two Quantity Question 3:
In a vessel, there is 60 litres mixture of acid and water. Then the ratio of acid and water is 7 : 5. How much water (in litres) is to be added to it so that the ratio of acid and water is 5: 9?
Answer (Detailed Solution Below)
To make a mixture from two Quantity Question 3 Detailed Solution
Given:
Initial mixture = 60 litres
Ratio of acid and water = 7:5
Formula Used:
Initial quantity of acid = (7/12) × 60
Initial quantity of water = (5/12) × 60
New quantity of water = Initial quantity of water + Added water
New ratio of acid and water = 5:9
Calculations:
Initial quantity of acid = (7/12) × 60 = 35 litres
Initial quantity of water = (5/12) × 60 = 25 litres
Let the added water be "x" litres
New quantity of water = 25 + x
According to the new ratio:
35/(25 + x) = 5/9
9 × 35 = 5 × (25 + x)
315 = 125 + 5x
5x = 315 - 125
5x = 190
x = 38
∴ The amount of water to be added is 38 litres
To make a mixture from two Quantity Question 4:
A container has 72 litre of pure milk. One-third of the milk is replaced by water in the container. Again, one-third of the mixture is extracted and an equal amount of water is added. What is the ratio of milk to water in the new mixture?
Answer (Detailed Solution Below)
To make a mixture from two Quantity Question 4 Detailed Solution
Given:
Initial volume of milk = 72 litres
One-third of the milk is replaced by water.
One-third of the mixture is extracted again, and an equal amount of water is added.
Formula used:
Pure liquid after repeated dilution = y [1 - (x)]n
n = number of times
x = fraction of quantity removed
Calculation:
Pure milk remains = 72 [1 - (1/3)]2
⇒ Pure milk remains = 72 × 4/9
⇒ Pure milk = 32
Water remaining = 72 - 32 = 40
⇒ Milk : Water = 32 : 40 = 4 : 5
⇒ Milk : Water = 4 : 5
∴ The correct answer is option (1).
To make a mixture from two Quantity Question 5:
A can contains a mixture of two liquids, grape juice and pineapple juice in the ratio 13 : 11. When 8 litres of the mixture is drawn off, and the can is filled with pineapple juice, the ratio becomes 13 : 14. How many litres of pineapple juice was initially contained in the can?
Answer (Detailed Solution Below)
To make a mixture from two Quantity Question 5 Detailed Solution
Given:
Initial ratio of Grape : Pineapple = 13 : 11
Mixture drawn off = 8 litres
Final ratio of Grape : Pineapple = 13 : 14
Formula Used:
Quantity of a component in mixture = (Ratio of component / Sum of ratios) × Total quantity of mixture
Calculation:
Let the initial total quantity of the mixture be 24x litres (13 + 11).
Initial quantity of grape juice = (13 / 24) × 24x = 13x litres
Initial quantity of pineapple juice = (11 / 24) × 24x = 11x litres
Quantity of grape juice drawn off = (13 / 24) × 8 = 13 / 3 litres
Quantity of pineapple juice drawn off = (11 / 24) × 8 = 11 / 3 litres
Remaining grape juice = 13x - 13/3 litres
Remaining pineapple juice = 11x - 11/3 litres
After adding 8 litres of pineapple juice, the quantity of pineapple juice becomes:
(11x - 11/3) + 8 litres
The new ratio of Grape : Pineapple is 13 : 14.
So, (13x - 13/3) / (11x - 11/3 + 8) = 13 / 14
⇒ 14 × (13x - 13/3) = 13 × (11x - 11/3 + 8)
⇒ 182x - 182/3 = 143x - 143/3 + 104
⇒ 39x = 104 + (182 - 143) / 3
⇒ 39x = 104 + 13
⇒ 39x = 117
⇒ x = 3
Initial quantity of pineapple juice = 11x = 11 × 3 = 33 litres
∴ The correct answer is Option (4).
Top To make a mixture from two Quantity MCQ Objective Questions
The ratio of two liquids B1 and B2 in a container is 3 ∶ 2. When 10 litres of mixture is removed from the container and is replaced with B2, the ratio of B1 and B2 becomes 3 ∶ 5. How many litres of B1 was in the container initially?
Answer (Detailed Solution Below)
To make a mixture from two Quantity Question 6 Detailed Solution
Download Solution PDFGiven:
Initial ratio B1 : B2 = 3 : 2
Mixture removed = 10 litres
Replaced with = B2
Final ratio B1 : B2 = 3 : 5
Formula Used:
Amount of B1 removed = (Ratio of B1 / Total ratio) × Quantity removed
Amount of B2 removed = (Ratio of B2 / Total ratio) × Quantity removed
Calculations:
Let initial quantity of B1 = 3x litres
Let initial quantity of B2 = 2x litres
Amount of B1 in 10 litres removed mixture = (3 / (3 + 2)) × 10 = (3/5) × 10 = 6 litres
Amount of B2 in 10 litres removed mixture = (2 / (3 + 2)) × 10 = (2/5) × 10 = 4 litres
Remaining B1 = 3x - 6
Remaining B2 = 2x - 4
After adding 10 litres of B2, final quantity of B2 = 2x - 4 + 10 = 2x + 6
Final ratio:
⇒ (3x - 6) / (2x + 6) = 3 / 5
⇒ 5 × (3x - 6) = 3 × (2x + 6)
⇒ 15x - 30 = 6x + 18
⇒ 9x = 48
⇒ x = 48 / 9 = 16 / 3
Initial quantity of B1 = 3x = 3 × (16 / 3) = 16 litres
∴ Initially, there were 16 litres of B1 in the container.
A jar contains a mixture of 2 liquids P and Q in the ratio 4:1. When 10 litres of the mixture is taken out and 10 litres of liquid Q is poured into the jar, the ratio becomes 2:3. How many litres of the liquid P was contained in the jar?
Answer (Detailed Solution Below)
To make a mixture from two Quantity Question 7 Detailed Solution
Download Solution PDFGiven:
A jar contains a mixture of two liquids P and Q in the ratio 4:1.
10 litres of the mixture is taken out, and 10 litres of liquid Q is added to the jar.
The new ratio becomes 2:3.
Formula used:
Let the initial quantity of liquid P be 4x and liquid Q be x.
After removing 10 litres of the mixture:
Liquid P removed = \(\frac{4}{5} \times 10\) = 8 litres.
Liquid Q removed = \(\frac{1}{5} \times 10\) = 2 litres.
The remaining quantities after removal:
Liquid P = 4x - 8.
Liquid Q = x - 2.
Adding 10 litres of liquid Q:
New liquid Q = (x - 2) + 10.
New ratio of P:Q = 2:3.
Equation: \(\frac{\text{Liquid P}}{\text{Liquid Q}} = \frac{2}{3}\)
Calculation:
\(\frac{4x - 8}{x - 2 + 10} = \frac{2}{3}\)
⇒ \(\frac{4x - 8}{x + 8} = \frac{2}{3}\)
⇒ 3(4x - 8) = 2(x + 8)
⇒ 12x - 24 = 2x + 16
⇒ 12x - 2x = 16 + 24
⇒ 10x = 40
⇒ x = 4
Initial liquid P = 4x = 4 × 4 = 16 litres.
∴ The correct answer is option (2).
To make a mixture from two Quantity Question 8:
The ratio of two liquids B1 and B2 in a container is 3 ∶ 2. When 10 litres of mixture is removed from the container and is replaced with B2, the ratio of B1 and B2 becomes 3 ∶ 5. How many litres of B1 was in the container initially?
Answer (Detailed Solution Below)
To make a mixture from two Quantity Question 8 Detailed Solution
Given:
Initial ratio B1 : B2 = 3 : 2
Mixture removed = 10 litres
Replaced with = B2
Final ratio B1 : B2 = 3 : 5
Formula Used:
Amount of B1 removed = (Ratio of B1 / Total ratio) × Quantity removed
Amount of B2 removed = (Ratio of B2 / Total ratio) × Quantity removed
Calculations:
Let initial quantity of B1 = 3x litres
Let initial quantity of B2 = 2x litres
Amount of B1 in 10 litres removed mixture = (3 / (3 + 2)) × 10 = (3/5) × 10 = 6 litres
Amount of B2 in 10 litres removed mixture = (2 / (3 + 2)) × 10 = (2/5) × 10 = 4 litres
Remaining B1 = 3x - 6
Remaining B2 = 2x - 4
After adding 10 litres of B2, final quantity of B2 = 2x - 4 + 10 = 2x + 6
Final ratio:
⇒ (3x - 6) / (2x + 6) = 3 / 5
⇒ 5 × (3x - 6) = 3 × (2x + 6)
⇒ 15x - 30 = 6x + 18
⇒ 9x = 48
⇒ x = 48 / 9 = 16 / 3
Initial quantity of B1 = 3x = 3 × (16 / 3) = 16 litres
∴ Initially, there were 16 litres of B1 in the container.
To make a mixture from two Quantity Question 9:
A can contains a mixture of two liquids, grape juice and pineapple juice in the ratio 13 : 11. When 8 litres of the mixture is drawn off, and the can is filled with pineapple juice, the ratio becomes 13 : 14. How many litres of pineapple juice was initially contained in the can?
Answer (Detailed Solution Below)
To make a mixture from two Quantity Question 9 Detailed Solution
Given:
Initial ratio of Grape : Pineapple = 13 : 11
Mixture drawn off = 8 litres
Final ratio of Grape : Pineapple = 13 : 14
Formula Used:
Quantity of a component in mixture = (Ratio of component / Sum of ratios) × Total quantity of mixture
Calculation:
Let the initial total quantity of the mixture be 24x litres (13 + 11).
Initial quantity of grape juice = (13 / 24) × 24x = 13x litres
Initial quantity of pineapple juice = (11 / 24) × 24x = 11x litres
Quantity of grape juice drawn off = (13 / 24) × 8 = 13 / 3 litres
Quantity of pineapple juice drawn off = (11 / 24) × 8 = 11 / 3 litres
Remaining grape juice = 13x - 13/3 litres
Remaining pineapple juice = 11x - 11/3 litres
After adding 8 litres of pineapple juice, the quantity of pineapple juice becomes:
(11x - 11/3) + 8 litres
The new ratio of Grape : Pineapple is 13 : 14.
So, (13x - 13/3) / (11x - 11/3 + 8) = 13 / 14
⇒ 14 × (13x - 13/3) = 13 × (11x - 11/3 + 8)
⇒ 182x - 182/3 = 143x - 143/3 + 104
⇒ 39x = 104 + (182 - 143) / 3
⇒ 39x = 104 + 13
⇒ 39x = 117
⇒ x = 3
Initial quantity of pineapple juice = 11x = 11 × 3 = 33 litres
∴ The correct answer is Option (4).
To make a mixture from two Quantity Question 10:
In a vessel, there is 60 litres mixture of acid and water. Then the ratio of acid and water is 7 : 5. How much water (in litres) is to be added to it so that the ratio of acid and water is 5: 9?
Answer (Detailed Solution Below)
To make a mixture from two Quantity Question 10 Detailed Solution
Given:
Initial mixture = 60 litres
Ratio of acid and water = 7:5
Formula Used:
Initial quantity of acid = (7/12) × 60
Initial quantity of water = (5/12) × 60
New quantity of water = Initial quantity of water + Added water
New ratio of acid and water = 5:9
Calculations:
Initial quantity of acid = (7/12) × 60 = 35 litres
Initial quantity of water = (5/12) × 60 = 25 litres
Let the added water be "x" litres
New quantity of water = 25 + x
According to the new ratio:
35/(25 + x) = 5/9
9 × 35 = 5 × (25 + x)
315 = 125 + 5x
5x = 315 - 125
5x = 190
x = 38
∴ The amount of water to be added is 38 litres
To make a mixture from two Quantity Question 11:
A container has 72 litre of pure milk. One-third of the milk is replaced by water in the container. Again, one-third of the mixture is extracted and an equal amount of water is added. What is the ratio of milk to water in the new mixture?
Answer (Detailed Solution Below)
To make a mixture from two Quantity Question 11 Detailed Solution
Given:
Initial volume of milk = 72 litres
One-third of the milk is replaced by water.
One-third of the mixture is extracted again, and an equal amount of water is added.
Formula used:
Pure liquid after repeated dilution = y [1 - (x)]n
n = number of times
x = fraction of quantity removed
Calculation:
Pure milk remains = 72 [1 - (1/3)]2
⇒ Pure milk remains = 72 × 4/9
⇒ Pure milk = 32
Water remaining = 72 - 32 = 40
⇒ Milk : Water = 32 : 40 = 4 : 5
⇒ Milk : Water = 4 : 5
∴ The correct answer is option (1).
To make a mixture from two Quantity Question 12:
A jar contains a mixture of 2 liquids P and Q in the ratio 4:1. When 10 litres of the mixture is taken out and 10 litres of liquid Q is poured into the jar, the ratio becomes 2:3. How many litres of the liquid P was contained in the jar?
Answer (Detailed Solution Below)
To make a mixture from two Quantity Question 12 Detailed Solution
Given:
A jar contains a mixture of two liquids P and Q in the ratio 4:1.
10 litres of the mixture is taken out, and 10 litres of liquid Q is added to the jar.
The new ratio becomes 2:3.
Formula used:
Let the initial quantity of liquid P be 4x and liquid Q be x.
After removing 10 litres of the mixture:
Liquid P removed = \(\frac{4}{5} \times 10\) = 8 litres.
Liquid Q removed = \(\frac{1}{5} \times 10\) = 2 litres.
The remaining quantities after removal:
Liquid P = 4x - 8.
Liquid Q = x - 2.
Adding 10 litres of liquid Q:
New liquid Q = (x - 2) + 10.
New ratio of P:Q = 2:3.
Equation: \(\frac{\text{Liquid P}}{\text{Liquid Q}} = \frac{2}{3}\)
Calculation:
\(\frac{4x - 8}{x - 2 + 10} = \frac{2}{3}\)
⇒ \(\frac{4x - 8}{x + 8} = \frac{2}{3}\)
⇒ 3(4x - 8) = 2(x + 8)
⇒ 12x - 24 = 2x + 16
⇒ 12x - 2x = 16 + 24
⇒ 10x = 40
⇒ x = 4
Initial liquid P = 4x = 4 × 4 = 16 litres.
∴ The correct answer is option (2).
To make a mixture from two Quantity Question 13:
Two equal glasses of the same type are respectively 1/3 and 1/4 full of milk. The glasses are then filled to the brim by adding water and the contents are mixed in a pot. What is the ratio of the content of water and milk in the pot?
Answer (Detailed Solution Below)
To make a mixture from two Quantity Question 13 Detailed Solution
Given:
Two equal glasses are 1/3 and 1/4 full of milk respectively, and then filled with water to the brim.
Formula used:
Ratio = (Volume of Water) : (Volume of Milk)
Calculations:
Let the capacity of each glass be 1 unit.
Volume of Milk in Glass 1 = 1/3
Volume of Water in Glass 1 = 1 - 1/3 = 2/3
Volume of Milk in Glass 2 = 1/4
Volume of Water in Glass 2 = 1 - 1/4 = 3/4
Total Milk = 1/3 + 1/4
⇒ Total Milk = \(\frac{4}{12} + \frac{3}{12} = \frac{7}{12}\)
Total Water = 2/3 + 3/4
⇒ Total Water = \(\frac{8}{12} + \frac{9}{12} = \frac{17}{12}\)
Ratio of Water : Milk = Total Water : Total Milk
⇒ Ratio = \(\frac{17}{12} : \frac{7}{12}\)
⇒ Ratio = 17 : 7
∴ The correct answer is option (4).