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Mixtures A and B are contained in two separate vessels. Mixture A contains ingredients P, Q and R in a ratio of 3 : 5 : 2 and mixture B contains ingredients P and Q in a ratio of 4 : 5. We have to make 540 litres of a new mixture by adding the mixtures A and B in a ratio of 1 : 2. What will be the quantity of ingredient P in the final mixture?
  • a)
    201 litres
  • b)
    210 litres
  • c)
    214 litres
  • d)
    231 litres
  • e)
    260 litres
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Mixtures A and B are contained in two separate vessels. Mixture A cont...
To solve this problem, we need to first calculate the quantities of ingredients P, Q, and R in mixtures A and B. Then, we can determine the amounts of these ingredients in the final mixture by using the given ratio.

Given:
Mixture A: P : Q : R = 3 : 5 : 2
Mixture B: P : Q = 4 : 5
Final mixture ratio: A : B = 1 : 2
Total mixture volume: 540 liters

Step 1: Calculate the quantities of ingredients in mixtures A and B.
Let's assume the quantities of ingredients P, Q, and R in mixture A are 3x, 5x, and 2x respectively (where x is a common factor).

In mixture A:
P = 3x
Q = 5x
R = 2x

In mixture B:
P = 4y (where y is a common factor)
Q = 5y

Step 2: Calculate the total quantity of mixture A and B in the final mixture.
Since the ratio of A : B in the final mixture is 1 : 2, we can assume the quantity of mixture A as 1z and the quantity of mixture B as 2z (where z is a common factor).

In the final mixture:
Mixture A = 1z
Mixture B = 2z

Step 3: Calculate the total volume of the final mixture.
The total volume of the final mixture is given as 540 liters.

1z + 2z = 540
3z = 540
z = 180

Step 4: Calculate the quantities of ingredients P, Q, and R in the final mixture.
In the final mixture:
Mixture A = 1z = 1 * 180 = 180 liters
Mixture B = 2z = 2 * 180 = 360 liters

Ingredient P:
In mixture A, P = 3x
In mixture B, P = 4y

By substituting the values of x and y:
In mixture A, P = 3 * (180/10) = 3 * 18 = 54 liters
In mixture B, P = 4 * (180/9) = 4 * 20 = 80 liters

Total quantity of ingredient P in the final mixture = P(A) + P(B) = 54 + 80 = 134 liters

Therefore, the correct answer is option 'C' - 134 liters.
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Mixtures A and B are contained in two separate vessels. Mixture A contains ingredients P, Q and R in a ratio of 3 : 5 : 2 and mixture B contains ingredients P and Q in a ratio of 4 : 5. We have to make 540 litres of a new mixture by adding the mixtures A and B in a ratio of 1 : 2. What will be the quantity of ingredient P in the final mixture?a)201 litresb)210 litresc)214 litresd)231 litrese)260 litresCorrect answer is option 'C'. Can you explain this answer?
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