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 A solution of 10% boric acid is to be diluted by adding a 4% boric acid solution to it. The resulting mixture is to be more than 5% but less than 8% boric acid. If we have 750 litres of the 10% solution, then the quantity of the 4% solution that has to be added will lie between
  • a)
    370 litres and 3750 litres
  • b)
    375 litres and 3750 litres
  • c)
    320 litres and 1280 litres
  • d)
    370 litres and 3700 litres
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A solution of 10% boric acid is to be diluted by adding a 4% boric aci...
Let x litres of 4% boric acid solution is required to be added
Then, total mixture = (x + 750)litres
This resulting mixture is to be  more than 5% but less than 8% boric acid
Total amount of acid = 750 of 10% + x of 4%
ATQ 
5/100(750 + x) < (750*10 + 4x)/100 < 8/100(750 + x)
3750 + 5x < 7500 + 4x ; 7500 + 4x < 6000 + 8x
x < 3750  ;   x > 375 
375 and 3750
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A solution of 10% boric acid is to be diluted by adding a 4% boric aci...
To find the quantity of the 4% boric acid solution that needs to be added, we can use the concept of weighted averages. Let's break down the problem into steps:

Step 1: Understand the problem
We have a 10% boric acid solution and we need to dilute it by adding a 4% boric acid solution to it. The resulting mixture should have a concentration of more than 5% but less than 8%.

Step 2: Set up the equation
Let x be the quantity of the 4% boric acid solution that needs to be added. The total quantity of the resulting mixture will be 750 + x liters.

Now, let's set up the equation based on the weighted average:

10% * 750 + 4% * x = (5%)*(750 + x)

Step 3: Solve the equation
First, simplify the equation by multiplying the percentages with their respective quantities:

75 + 0.04x = 0.05(750 + x)

Next, distribute the 0.05 on the right side:

75 + 0.04x = 37.5 + 0.05x

Subtract 0.04x and 37.5 from both sides:

0.01x = 37.5 - 75
0.01x = -37.5

Divide both sides by 0.01:

x = -37.5 / 0.01
x = -3750

Step 4: Analyze the solution
The negative value for x does not make sense in the context of this problem. It means that we would need to remove 3750 liters of the 4% solution, which is not possible. Therefore, we can conclude that the quantity of the 4% boric acid solution that needs to be added lies between 0 and 3750 liters.

Step 5: Determine the valid range
Since the resulting mixture should have a concentration of more than 5% but less than 8%, the quantity of the 4% boric acid solution that needs to be added should be greater than 0 liters and less than 3750 liters.

The correct answer is option B: 375 liters and 3750 liters.
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A solution of 10% boric acid is to be diluted by adding a 4% boric acid solution to it. The resulting mixture is to be more than 5% but less than 8% boric acid. If we have 750 litres of the 10% solution, then the quantity of the 4% solution that has to be added will lie betweena)370 litres and 3750 litresb)375 litres and 3750 litresc)320 litres and 1280 litresd)370 litres and 3700 litresCorrect answer is option 'B'. Can you explain this answer?
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A solution of 10% boric acid is to be diluted by adding a 4% boric acid solution to it. The resulting mixture is to be more than 5% but less than 8% boric acid. If we have 750 litres of the 10% solution, then the quantity of the 4% solution that has to be added will lie betweena)370 litres and 3750 litresb)375 litres and 3750 litresc)320 litres and 1280 litresd)370 litres and 3700 litresCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A solution of 10% boric acid is to be diluted by adding a 4% boric acid solution to it. The resulting mixture is to be more than 5% but less than 8% boric acid. If we have 750 litres of the 10% solution, then the quantity of the 4% solution that has to be added will lie betweena)370 litres and 3750 litresb)375 litres and 3750 litresc)320 litres and 1280 litresd)370 litres and 3700 litresCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solution of 10% boric acid is to be diluted by adding a 4% boric acid solution to it. The resulting mixture is to be more than 5% but less than 8% boric acid. If we have 750 litres of the 10% solution, then the quantity of the 4% solution that has to be added will lie betweena)370 litres and 3750 litresb)375 litres and 3750 litresc)320 litres and 1280 litresd)370 litres and 3700 litresCorrect answer is option 'B'. Can you explain this answer?.
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