Question

A vessel contains total 95 litre mixture of milk & water in the ratio 15 : 4 respectively P litre of mixture taken out from the vessel and 18 litres water added in the remaining mixture, then the new ratio of milk to water becomes 3 : 2, find the value of P?

• A. 57
• B. 19
• C. 27.5
• D. 38

Hint:

For problems involving mixtures and ratios, set up the initial conditions and equations carefully to solve for the unknown quantity.

Answer 1

The Correct Option is D

Step 1: Set up the initial conditions. 
Let the total mixture be 95 litres with milk and water in the ratio 15:4. Therefore, the amount of milk is: 
\[ \text{Milk} = \frac{15}{19} \times 95 = 75 \, \text{litres}. \] The amount of water is: 
\[ \text{Water} = \frac{4}{19} \times 95 = 20 \, \text{litres}. \]

Step 2: Remove P litres of the mixture. 
When P litres of the mixture is removed, the amounts of milk and water removed are in the same ratio (15:4). Hence, the amount of milk removed is: 
\[ \text{Milk removed} = \frac{15}{19} \times P, \text{Water removed} = \frac{4}{19} \times P. \]

Step 3: Add 18 litres of water. 
After removing P litres of the mixture, 18 litres of water is added to the remaining mixture. So, the new amount of water becomes: 
\[ \text{New water} = 20 - \frac{4}{19} \times P + 18. \]

Step 4: Set up the new ratio. 
We are told that the new ratio of milk to water becomes 3:2. So, we set up the equation: 
\[ \frac{75 - \frac{15}{19} \times P}{20 - \frac{4}{19} \times P + 18} = \frac{3}{2}. \]

Step 5: Solve for P. 
Simplifying the equation: 
\[ \frac{75 - \frac{15}{19} \times P}{38 - \frac{4}{19} \times P} = \frac{3}{2} \Rightarrow 2 \times (75 - \frac{15}{19} \times P) = 3 \times (38 - \frac{4}{19} \times P). \] Expanding both sides: 
\[ 150 - \frac{30}{19} \times P = 114 - \frac{12}{19} \times P. \] Simplifying: 
\[ 150 - 114 = \frac{30}{19} \times P - \frac{12}{19} \times P \Rightarrow 36 = \frac{18}{19} \times P. \] Solving for P: 
\[ P = \frac{36 \times 19}{18} = 38. \]

Step 6: Conclusion. 
Thus, the value of P is 38 litres, and the correct answer is (d).