Liquid A,B were mixed in equal proportion in vessel X to form 200 liter mixture. 50 l of liquid C was added to mixture in vessel X. 100 l of this mixture was taken out and put in vessel Y. If 20 l of liquid D was added to the mixture in vessel Y, what is percentage of liquid C in vessel Y?

Options

A. 16.67
B. 18.5
C. 15.75
D. 22.5

Answer

To solve the problem step by step, let's break it down into manageable parts.

### Step 1: Determine the composition of the mixture in vessel X.
- Liquid A and Liquid B are mixed in equal proportions to form a total of 200 liters.
- Therefore, the quantity of Liquid A = 100 liters and the quantity of Liquid B = 100 liters.

### Step 2: Add Liquid C to the mixture in vessel X.
- 50 liters of Liquid C is added to the 200 liters mixture in vessel X.
- Now, the total mixture in vessel X = 200 liters (A + B) + 50 liters (C) = 250 liters.
- The composition of the mixture in vessel X is:
- Liquid A: 100 liters
- Liquid B: 100 liters
- Liquid C: 50 liters

### Step 3: Calculate the proportions of each liquid in the mixture.
- The total volume of the mixture is 250 liters.
- The proportions of each liquid in the mixture can be calculated as follows:
- Proportion of A = 100/250 = 2/5
- Proportion of B = 100/250 = 2/5
- Proportion of C = 50/250 = 1/5

### Step 4: Transfer 100 liters of the mixture from vessel X to vessel Y.
- When 100 liters of the mixture is taken out, the quantities of each liquid transferred to vessel Y are:
- Liquid A = (2/5) * 100 liters = 40 liters
- Liquid B = (2/5) * 100 liters = 40 liters
- Liquid C = (1/5) * 100 liters = 20 liters

### Step 5: Add Liquid D to the mixture in vessel Y.
- After transferring the 100 liters to vessel Y, 20 liters of Liquid D is added.
- The total mixture in vessel Y now consists of:
- Liquid A = 40 liters
- Liquid B = 40 liters
- Liquid C = 20 liters
- Liquid D = 20 liters
- Total volume in vessel Y = 40 + 40 + 20 + 20 = 120 liters.

### Step 6: Calculate the percentage of Liquid C in vessel Y.
- The percentage of Liquid C in vessel Y is calculated as follows:
\[ \text{Percentage of Liquid C} = \left( \frac{\text{Quantity of Liquid C}}{\text{Total Quantity in Vessel Y}} \right) \times 100 \]
\[ = \left( \frac{20}{120} \right) \times 100 = \frac{2000}{120} = \frac{50}{3} \approx 16.67\% \]

### Final Answer:
The percentage of Liquid C in vessel Y is approximately **16.67%**.

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