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A beaker contains acid and water in the ratio 1 : x, respectively. When 300 ml of the mixture and 50 ml of water are mixed, the ratio of acid to water becomes 2 : 5. What is the value of x?
- a)2
- b)1
- c)3
- d)4
Correct answer is option 'A'. Can you explain this answer?
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A beaker contains acid and water in the ratio 1 : x, respectively. Wh...
Given:
- The ratio of acid and water in the beaker = 1:x
- When 300 ml of the mixture and 50 ml of water are mixed, the ratio of acid to water becomes 2:5
To find: The value of x
Solution:
Let's assume that the beaker initially contains 1L of the mixture.
- The ratio of acid and water in the beaker = 1:x
So, the beaker initially contains acid = 1/ (1+x) L and water = x / (1+x) L.
- When 300 ml of the mixture and 50 ml of water are mixed, the ratio of acid to water becomes 2:5
Let's calculate the amount of acid and water in 300 ml of the initial mixture.
- Acid = (1/(1+x)) * (300/1000) = 3/(10*(1+x))
- Water = (x/(1+x)) * (300/1000) = 3x/(10*(1+x))
Now, when 300 ml of the mixture and 50 ml of water are mixed, the total amount of water becomes (3x + 50)/1000 L and the total amount of acid becomes (3/(10*(1+x))) L.
So, the ratio of acid to water becomes:
- (3/(10*(1+x))) / ((3x + 50)/1000) = 2/5
Solving this equation, we get:
- x = 2
Therefore, the value of x is 2.
Hence, option A is the correct answer.
- The ratio of acid and water in the beaker = 1:x
- When 300 ml of the mixture and 50 ml of water are mixed, the ratio of acid to water becomes 2:5
To find: The value of x
Solution:
Let's assume that the beaker initially contains 1L of the mixture.
- The ratio of acid and water in the beaker = 1:x
So, the beaker initially contains acid = 1/ (1+x) L and water = x / (1+x) L.
- When 300 ml of the mixture and 50 ml of water are mixed, the ratio of acid to water becomes 2:5
Let's calculate the amount of acid and water in 300 ml of the initial mixture.
- Acid = (1/(1+x)) * (300/1000) = 3/(10*(1+x))
- Water = (x/(1+x)) * (300/1000) = 3x/(10*(1+x))
Now, when 300 ml of the mixture and 50 ml of water are mixed, the total amount of water becomes (3x + 50)/1000 L and the total amount of acid becomes (3/(10*(1+x))) L.
So, the ratio of acid to water becomes:
- (3/(10*(1+x))) / ((3x + 50)/1000) = 2/5
Solving this equation, we get:
- x = 2
Therefore, the value of x is 2.
Hence, option A is the correct answer.
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Community Answer
A beaker contains acid and water in the ratio 1 : x, respectively. Wh...
In 300 ml of mixture
Therefore,
14x + 2 = 30
14x = 28
x = 2
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