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Two solutions of 90% and 97% purity are mixed resulting in 21 litres of the mixture of 94% purity. How much is the quantity of the first solution in the resulting mixture?
- a)15 litres
- b)12 litres
- c)9 litres
- d)6 litres
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Two solutions of 90% and 97% purity are mixed resulting in 21 litres o...
Let the x litre is the quantity of first solution in the resulting mixture
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Two solutions of 90% and 97% purity are mixed resulting in 21 litres o...
Problem: Two solutions of 90% and 97% purity are mixed resulting in 21 litres of the mixture of 94% purity. How much is the quantity of the first solution in the resulting mixture?
Solution:
Let x be the quantity of the first solution (90% purity) in the mixture.
Then (21 - x) is the quantity of the second solution (97% purity) in the mixture.
The amount of pure substance in the first solution is 0.9x.
The amount of pure substance in the second solution is 0.97(21 - x).
The total amount of pure substance in the mixture is 0.94(21).
Therefore, we have the equation:
0.9x + 0.97(21 - x) = 0.94(21)
Simplifying and solving for x, we get:
0.9x + 20.37 - 0.97x = 19.74
0.07x = 0.63
x = 9
Therefore, the quantity of the first solution in the resulting mixture is 9 litres (option c).
Note: The solution involves simple algebraic equations. We can apply the concept of the amount of pure substance in each solution and the total amount of pure substance in the mixture to solve the problem.
Solution:
Let x be the quantity of the first solution (90% purity) in the mixture.
Then (21 - x) is the quantity of the second solution (97% purity) in the mixture.
The amount of pure substance in the first solution is 0.9x.
The amount of pure substance in the second solution is 0.97(21 - x).
The total amount of pure substance in the mixture is 0.94(21).
Therefore, we have the equation:
0.9x + 0.97(21 - x) = 0.94(21)
Simplifying and solving for x, we get:
0.9x + 20.37 - 0.97x = 19.74
0.07x = 0.63
x = 9
Therefore, the quantity of the first solution in the resulting mixture is 9 litres (option c).
Note: The solution involves simple algebraic equations. We can apply the concept of the amount of pure substance in each solution and the total amount of pure substance in the mixture to solve the problem.
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Two solutions of 90% and 97% purity are mixed resulting in 21 litres of the mixture of 94% purity. How much is the quantity of the first solution in the resulting mixture?a)15 litresb)12 litresc)9 litresd)6 litrese)None of theseCorrect answer is option 'C'. Can you explain this answer?
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