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A certain tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride.
The proportion of sodium chloride in the tank is 40% by volume and the capacity of the tank is 24 gallons. If
the water evaporates from the tank at the rate of 0.5 gallons per hour, and the amount of sodium chloride
stays the same, what will be the concentration of water in the mixture in 2 hours?
The proportion of sodium chloride in the tank is 40% by volume and the capacity of the tank is 24 gallons. If
the water evaporates from the tank at the rate of 0.5 gallons per hour, and the amount of sodium chloride
stays the same, what will be the concentration of water in the mixture in 2 hours?
- a)43%
- b)50%
- c)52%
- d)54%
- e)56%
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A certain tank is filled to one quarter of its capacity with a mixture...
First, let’s find the initial amount of water in the tank:
Total mixture in the tank =1/4 × (capacity of the tank) = (1/4) × 24 = 6 gallons
Concentration of water in the mixture = 100% – (concentration of sodium chloride) = 100% – 40% = 60%
Initial amount of water in the tank = 60% × (total mixture)= 0.6 × 6 = 3.6 gallons
Total mixture in the tank =1/4 × (capacity of the tank) = (1/4) × 24 = 6 gallons
Concentration of water in the mixture = 100% – (concentration of sodium chloride) = 100% – 40% = 60%
Initial amount of water in the tank = 60% × (total mixture)= 0.6 × 6 = 3.6 gallons
Next, let’s find the amount and concentration of water after 2 hours:
Amount of water that will evaporate in 2 hours = (rate of evaporation)(time) = 0.5(2) = 1 gallon
Remaining amount of water = initial amount – evaporated water = 3.6 – 1 = 2.6 gallons
Remaining amount of mixture = initial amount – evaporated water = 6 – 1 = 5 gallons
Concentration of water in the mixture in 2 hours =
The correct answer is C.
Amount of water that will evaporate in 2 hours = (rate of evaporation)(time) = 0.5(2) = 1 gallon
Remaining amount of water = initial amount – evaporated water = 3.6 – 1 = 2.6 gallons
Remaining amount of mixture = initial amount – evaporated water = 6 – 1 = 5 gallons
Concentration of water in the mixture in 2 hours =
The correct answer is C.
Most Upvoted Answer
A certain tank is filled to one quarter of its capacity with a mixture...
Given information:
- Tank capacity: 24 gallons
- Tank filled with mixture of water and sodium chloride
- Proportion of sodium chloride in the tank: 40% by volume
- Water evaporates at a rate of 0.5 gallons per hour
- Sodium chloride amount remains the same
To find: Concentration of water in the mixture after 2 hours
Let's break down the problem into steps:
Step 1: Find the initial amount of water and sodium chloride in the tank
- The tank is filled to one quarter of its capacity, so the initial amount of liquid in the tank is 1/4 * 24 = 6 gallons.
- The proportion of sodium chloride in the tank is 40%, so the initial amount of sodium chloride in the tank is 40% of 6 gallons = 0.4 * 6 = 2.4 gallons.
- Therefore, the initial amount of water in the tank is 6 - 2.4 = 3.6 gallons.
Step 2: Calculate the amount of water remaining after 2 hours
- Water evaporates at a rate of 0.5 gallons per hour, so after 2 hours, 0.5 * 2 = 1 gallon of water will have evaporated.
- Therefore, the amount of water remaining in the tank after 2 hours is 3.6 - 1 = 2.6 gallons.
Step 3: Calculate the new total volume of the mixture after 2 hours
- The amount of sodium chloride remains the same at 2.4 gallons.
- The amount of water remaining after 2 hours is 2.6 gallons.
- Therefore, the new total volume of the mixture after 2 hours is 2.4 + 2.6 = 5 gallons.
Step 4: Calculate the concentration of water in the mixture after 2 hours
- The concentration of water is the proportion of water in the total volume of the mixture.
- The proportion of water in the mixture after 2 hours is 2.6 / 5 * 100% = 52%.
Therefore, the concentration of water in the mixture after 2 hours is 52%. Hence, the correct answer is option C.
- Tank capacity: 24 gallons
- Tank filled with mixture of water and sodium chloride
- Proportion of sodium chloride in the tank: 40% by volume
- Water evaporates at a rate of 0.5 gallons per hour
- Sodium chloride amount remains the same
To find: Concentration of water in the mixture after 2 hours
Let's break down the problem into steps:
Step 1: Find the initial amount of water and sodium chloride in the tank
- The tank is filled to one quarter of its capacity, so the initial amount of liquid in the tank is 1/4 * 24 = 6 gallons.
- The proportion of sodium chloride in the tank is 40%, so the initial amount of sodium chloride in the tank is 40% of 6 gallons = 0.4 * 6 = 2.4 gallons.
- Therefore, the initial amount of water in the tank is 6 - 2.4 = 3.6 gallons.
Step 2: Calculate the amount of water remaining after 2 hours
- Water evaporates at a rate of 0.5 gallons per hour, so after 2 hours, 0.5 * 2 = 1 gallon of water will have evaporated.
- Therefore, the amount of water remaining in the tank after 2 hours is 3.6 - 1 = 2.6 gallons.
Step 3: Calculate the new total volume of the mixture after 2 hours
- The amount of sodium chloride remains the same at 2.4 gallons.
- The amount of water remaining after 2 hours is 2.6 gallons.
- Therefore, the new total volume of the mixture after 2 hours is 2.4 + 2.6 = 5 gallons.
Step 4: Calculate the concentration of water in the mixture after 2 hours
- The concentration of water is the proportion of water in the total volume of the mixture.
- The proportion of water in the mixture after 2 hours is 2.6 / 5 * 100% = 52%.
Therefore, the concentration of water in the mixture after 2 hours is 52%. Hence, the correct answer is option C.
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A certain tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride.The proportion of sodium chloride in the tank is 40% by volume and the capacity of the tank is 24 gallons. Ifthe water evaporates from the tank at the rate of 0.5 gallons per hour, and the amount of sodium chloridestays the same, what will be the concentration of water in the mixture in 2 hours?a)43%b)50%c)52%d)54%e)56%Correct answer is option 'C'. Can you explain this answer?
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A certain tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride.The proportion of sodium chloride in the tank is 40% by volume and the capacity of the tank is 24 gallons. Ifthe water evaporates from the tank at the rate of 0.5 gallons per hour, and the amount of sodium chloridestays the same, what will be the concentration of water in the mixture in 2 hours?a)43%b)50%c)52%d)54%e)56%Correct answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A certain tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride.The proportion of sodium chloride in the tank is 40% by volume and the capacity of the tank is 24 gallons. Ifthe water evaporates from the tank at the rate of 0.5 gallons per hour, and the amount of sodium chloridestays the same, what will be the concentration of water in the mixture in 2 hours?a)43%b)50%c)52%d)54%e)56%Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride.The proportion of sodium chloride in the tank is 40% by volume and the capacity of the tank is 24 gallons. Ifthe water evaporates from the tank at the rate of 0.5 gallons per hour, and the amount of sodium chloridestays the same, what will be the concentration of water in the mixture in 2 hours?a)43%b)50%c)52%d)54%e)56%Correct answer is option 'C'. Can you explain this answer?.
A certain tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride.The proportion of sodium chloride in the tank is 40% by volume and the capacity of the tank is 24 gallons. Ifthe water evaporates from the tank at the rate of 0.5 gallons per hour, and the amount of sodium chloridestays the same, what will be the concentration of water in the mixture in 2 hours?a)43%b)50%c)52%d)54%e)56%Correct answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A certain tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride.The proportion of sodium chloride in the tank is 40% by volume and the capacity of the tank is 24 gallons. Ifthe water evaporates from the tank at the rate of 0.5 gallons per hour, and the amount of sodium chloridestays the same, what will be the concentration of water in the mixture in 2 hours?a)43%b)50%c)52%d)54%e)56%Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride.The proportion of sodium chloride in the tank is 40% by volume and the capacity of the tank is 24 gallons. Ifthe water evaporates from the tank at the rate of 0.5 gallons per hour, and the amount of sodium chloridestays the same, what will be the concentration of water in the mixture in 2 hours?a)43%b)50%c)52%d)54%e)56%Correct answer is option 'C'. Can you explain this answer?.
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