A 60-litre solution of milk and water is mixed in the ratio 3:1. Then, 8 litres of this mixture is removed. After that, p litres of milk and q litres of water are added. The resulting mixture has milk and water in a 9:5 ratio. Given that p + q = 11, find the difference between p and q.

Calculation

Initial mixture (60 litres in 3:1 ratio)

Milk = (3/4) × 60 = 45 litres

Water = (1/4) × 60 = 15 litres

8 litres of mixture removed
Ratio = 3:1 → in 8 litres:

Milk removed = (3/4) × 8 = 6 litres

Water removed = (1/4) × 8 = 2 litres

Remaining:

Milk = 45 - 6 = 39 litres

Water = 15 - 2 = 13 litres

Add p litres of milk and q litres of water
Final milk = 39 + p
Final water = 13 + q

New ratio = (39 + p) / (13 + q) = 9 / 5
So, 5(39 + p) = 9(13 + q)
So, 195 + 5p = 117 + 9q
=> 5p - 9q = -78 → [Equation 1]
Also, p + q = 11 → [Equation 2]

From Equation 2: p = 11 - q
Substitute into Equation 1:
5(11 - q) - 9q = -78
So, 55 - 5q - 9q = -78
So, 55 - 14q = -78
=> -14q = -133
=> q = 9.5
=> p = 11 - 9.5 = 1.5

Difference between p and q is 9.5 – 1.5 = 8