Container A contains 54 litres of a milk-water mixture in the ratio 8:1 (milk:water). From container A, 18 litres of the mixture is taken out and poured into container B, in which initially the ratio of milk to water is 3:1. After this transfer, the difference between total milk and total water in container B becomes 30 litres. Find the quantity (in litres) of the initial mixture in container B before the transfer.

Introduction / Context:
This is a multi-step transfer mixture problem. The mixture taken from container A keeps the same milk-water ratio as in A, so you must first compute how much milk and how much water is inside the 18 litres transferred. Then, represent container B initial milk and water in terms of an unknown initial volume. After adding the transferred milk and water, use the given final condition (milk minus water equals 30 litres) to form an equation and solve for the initial volume in B.

Given Data / Assumptions:

• Container A total = 54 litres, milk:water = 8:1
• Transferred from A to B = 18 litres (same composition as A)
• Container B initial milk:water = 3:1
• After transfer in B: (milk - water) = 30 litres
• Let initial volume in B = V litres

Concept / Approach:
Convert ratios into actual quantities. For A, use parts to get milk and water per litre. For the transferred 18 litres, scale down from the 54 litres or directly use the 8:1 ratio. For B, write initial milk and water as fractions of V based on 3:1. Add transferred amounts, then apply the difference condition to solve for V.

Step-by-Step Solution:
In A, total parts = 8 + 1 = 9 Milk in A = (8/9) * 54 = 48 litres Water in A = (1/9) * 54 = 6 litres 18 litres is 18/54 = 1/3 of A, so transferred milk = 48*(1/3)=16 and transferred water = 6*(1/3)=2 In B initially (3:1): milk = (3/4)V and water = (1/4)V After transfer: milk = (3/4)V + 16, water = (1/4)V + 2 Given milk - water = 30: ((3/4)V + 16) - ((1/4)V + 2) = 30 (1/2)V + 14 = 30 (1/2)V = 16 V = 32 litres

Verification / Alternative check:
If V=32, initial milk in B=24 and water=8. After adding 16 milk and 2 water, final milk=40 and final water=10. Difference is 40 - 10 = 30, which matches the condition.

Why Other Options Are Wrong:
24, 28, 30 give smaller final differences when checked with the same transfer amounts. 36 gives a larger final difference than 30 after transfer.

Common Pitfalls:
Assuming the 18 litres transferred is pure milk or pure water, forgetting that the transferred mixture keeps the same ratio as A, or using the final condition as a ratio instead of a difference.

Final Answer:
The initial quantity of mixture in container B was 32 litres.