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A chemist has one solution containing 50% acid and a second one containing 25% acid. How much of each should be used respectively to make 10 litres of a 40% acid solution?
- a)6 litres, 4 litres
- b)2 litres, 6 litres
- c)4 litres, 6 litres
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A chemist has one solution containing 50% acid and a second one contai...
Let x litres of the 40% solution be mixed with y litres of 25% solution.
then x + y = 10 ...(1)
50% of x + 25% of y = 40% of 10
⇒ 50x + 25y = 400
⇒ 2x + y = 16 ...(2)
From (1) and (2)
∴ x = 10 - 4 = 6
then x + y = 10 ...(1)
50% of x + 25% of y = 40% of 10
⇒ 50x + 25y = 400
⇒ 2x + y = 16 ...(2)
From (1) and (2)
∴ x = 10 - 4 = 6
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Community Answer
A chemist has one solution containing 50% acid and a second one contai...
Understanding the Problem
To create a 10-litre solution with 40% acid, we need to combine two solutions: one that has 50% acid and another with 25% acid. We need to determine how much of each solution to mix.
Let’s Define the Variables
- Let x = litres of the 50% acid solution.
- Let y = litres of the 25% acid solution.
We know that:
- The total volume of the mixture: x + y = 10 litres.
Setting Up the Equations
To find the amount of acid in each solution:
- Acid from 50% solution: 0.50x
- Acid from 25% solution: 0.25y
We want the total acid to equal 40% of the final solution:
- Total acid in the mixture: 0.40 * 10 = 4 litres.
Thus, we can set up the second equation:
- 0.50x + 0.25y = 4 litres.
Solving the Equations
Now we have a system of equations:
1. x + y = 10
2. 0.50x + 0.25y = 4
We can solve the first equation for y:
- y = 10 - x.
Now substitute y in the second equation:
- 0.50x + 0.25(10 - x) = 4
This simplifies to:
- 0.50x + 2.5 - 0.25x = 4
Combine like terms:
- 0.25x + 2.5 = 4
Subtract 2.5 from both sides:
- 0.25x = 1.5
Multiply both sides by 4:
- x = 6 litres.
Now substitute back to find y:
- y = 10 - 6 = 4 litres.
Conclusion
Thus, the chemist should use:
- 6 litres of the 50% acid solution.
- 4 litres of the 25% acid solution.
The correct option is a) 6 litres, 4 litres.
To create a 10-litre solution with 40% acid, we need to combine two solutions: one that has 50% acid and another with 25% acid. We need to determine how much of each solution to mix.
Let’s Define the Variables
- Let x = litres of the 50% acid solution.
- Let y = litres of the 25% acid solution.
We know that:
- The total volume of the mixture: x + y = 10 litres.
Setting Up the Equations
To find the amount of acid in each solution:
- Acid from 50% solution: 0.50x
- Acid from 25% solution: 0.25y
We want the total acid to equal 40% of the final solution:
- Total acid in the mixture: 0.40 * 10 = 4 litres.
Thus, we can set up the second equation:
- 0.50x + 0.25y = 4 litres.
Solving the Equations
Now we have a system of equations:
1. x + y = 10
2. 0.50x + 0.25y = 4
We can solve the first equation for y:
- y = 10 - x.
Now substitute y in the second equation:
- 0.50x + 0.25(10 - x) = 4
This simplifies to:
- 0.50x + 2.5 - 0.25x = 4
Combine like terms:
- 0.25x + 2.5 = 4
Subtract 2.5 from both sides:
- 0.25x = 1.5
Multiply both sides by 4:
- x = 6 litres.
Now substitute back to find y:
- y = 10 - 6 = 4 litres.
Conclusion
Thus, the chemist should use:
- 6 litres of the 50% acid solution.
- 4 litres of the 25% acid solution.
The correct option is a) 6 litres, 4 litres.
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A chemist has one solution containing 50% acid and a second one containing 25% acid. How much of each should be used respectively to make 10 litres of a 40% acid solution?a)6 litres, 4 litresb)2 litres, 6 litresc)4 litres, 6 litresd)None of theseCorrect answer is option 'A'. Can you explain this answer?
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A chemist has one solution containing 50% acid and a second one containing 25% acid. How much of each should be used respectively to make 10 litres of a 40% acid solution?a)6 litres, 4 litresb)2 litres, 6 litresc)4 litres, 6 litresd)None of theseCorrect answer is option 'A'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A chemist has one solution containing 50% acid and a second one containing 25% acid. How much of each should be used respectively to make 10 litres of a 40% acid solution?a)6 litres, 4 litresb)2 litres, 6 litresc)4 litres, 6 litresd)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A chemist has one solution containing 50% acid and a second one containing 25% acid. How much of each should be used respectively to make 10 litres of a 40% acid solution?a)6 litres, 4 litresb)2 litres, 6 litresc)4 litres, 6 litresd)None of theseCorrect answer is option 'A'. Can you explain this answer?.
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