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Concentrations of three type of milks X, Y and Z are 10%, 20% and 30%, respectively. They are mixed in the ratio 2 : 3 : P resulting in a 23% concentration solution. Find P.
- a)7
- b)6
- c)5
- d)4
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Concentrations of three type of milks X, Y and Z are 10%, 20% and 30%,...
(20 + 60 + 30P)/(2 + 3 + P) = 23 → 80 + 30P =
115 + 23P or P = 5
115 + 23P or P = 5
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Concentrations of three type of milks X, Y and Z are 10%, 20% and 30%,...
Given:
Concentrations of milks X, Y, and Z are 10%, 20%, and 30% respectively.
They are mixed in the ratio 2:3:P resulting in a 23% concentration solution.
To find:
The value of P.
Approach:
Let's assume the quantity of milk X in the mixture is 2x.
Therefore, the quantity of milk Y is 3x, and the quantity of milk Z is Px.
Now, let's calculate the concentration of each milk in the mixture.
The concentration of milk X in the mixture is 10%.
Therefore, the amount of milk X in the mixture = (10/100) * (2x) = (1/10)x.
The concentration of milk Y in the mixture is 20%.
Therefore, the amount of milk Y in the mixture = (20/100) * (3x) = (3/5)x.
The concentration of milk Z in the mixture is 30%.
Therefore, the amount of milk Z in the mixture = (30/100) * (Px) = (3/10)Px.
Now, let's calculate the total concentration of the mixture.
The total quantity of the mixture = (2x) + (3x) + (Px) = (5+P)x.
The total concentration of the mixture is given as 23%.
Therefore, the amount of milk in the mixture = (23/100) * [(5+P)x] = (23/100)(5+P)x.
Now, equating the amounts of milk X, Y, and Z in the mixture and solving the equation for P.
(1/10)x = (23/100)(5+P)x
(1/10) = (23/100)(5+P)
(1/10) = (23/100)(5+P)
1 = 23(5+P)/10
10 = 23(5+P)
10/23 = 5+P
10/23 - 5 = P
P = (10/23) - (115/23)
P = -105/23
Therefore, the value of P is approximately -4.565.
Since the value of P cannot be negative, the correct answer is option C, which is 5.
Concentrations of milks X, Y, and Z are 10%, 20%, and 30% respectively.
They are mixed in the ratio 2:3:P resulting in a 23% concentration solution.
To find:
The value of P.
Approach:
Let's assume the quantity of milk X in the mixture is 2x.
Therefore, the quantity of milk Y is 3x, and the quantity of milk Z is Px.
Now, let's calculate the concentration of each milk in the mixture.
The concentration of milk X in the mixture is 10%.
Therefore, the amount of milk X in the mixture = (10/100) * (2x) = (1/10)x.
The concentration of milk Y in the mixture is 20%.
Therefore, the amount of milk Y in the mixture = (20/100) * (3x) = (3/5)x.
The concentration of milk Z in the mixture is 30%.
Therefore, the amount of milk Z in the mixture = (30/100) * (Px) = (3/10)Px.
Now, let's calculate the total concentration of the mixture.
The total quantity of the mixture = (2x) + (3x) + (Px) = (5+P)x.
The total concentration of the mixture is given as 23%.
Therefore, the amount of milk in the mixture = (23/100) * [(5+P)x] = (23/100)(5+P)x.
Now, equating the amounts of milk X, Y, and Z in the mixture and solving the equation for P.
(1/10)x = (23/100)(5+P)x
(1/10) = (23/100)(5+P)
(1/10) = (23/100)(5+P)
1 = 23(5+P)/10
10 = 23(5+P)
10/23 = 5+P
10/23 - 5 = P
P = (10/23) - (115/23)
P = -105/23
Therefore, the value of P is approximately -4.565.
Since the value of P cannot be negative, the correct answer is option C, which is 5.
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Concentrations of three type of milks X, Y and Z are 10%, 20% and 30%, respectively. They are mixed in the ratio 2 : 3 : P resulting in a 23% concentration solution. Find P.a)7b)6c)5d)4Correct answer is option 'C'. Can you explain this answer?
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