Mixture Problem: Find the Value of P

Total mixture = 95 L

Initial ratio of milk : water = 15 : 4

Milk = $\frac{15}{19} \times 95 = 75 \, \text{L}$
Water = $\frac{4}{19} \times 95 = 20 \, \text{L}$

Step 1: Let P litres of mixture be removed

Milk removed = $\frac{15}{19} \times P = \frac{15P}{19}$
Water removed = $\frac{4}{19} \times P = \frac{4P}{19}$

Remaining milk = $75 - \frac{15P}{19}$
Remaining water = $20 - \frac{4P}{19}$

After adding 18 L of water:
New water = $20 - \frac{4P}{19} + 18 = 38 - \frac{4P}{19}$

Step 2: According to the new ratio

$\frac{75 - \frac{15P}{19}}{38 - \frac{4P}{19}} = \frac{3}{2}$

Step 3: Cross multiply

$2 \left( 75 - \frac{15P}{19} \right) = 3 \left( 38 - \frac{4P}{19} \right)$

$150 - \frac{30P}{19} = 114 - \frac{12P}{19}$

$36 = \frac{18P}{19}$

$P = \frac{36 \times 19}{18} = \boxed{38}$

✅ Final Answer: P = 38 litres