A tin contains a mixture of two liquids A and B in the ratio 4:1. If 45 litres of this mixture is removed and replaced with 45 litres of liquid B, the new ratio of A to B becomes 2:5. What is the total capacity of the tin?

Step 1: Let the total capacity of the tin be x litres

• The initial ratio of liquids A and B = 4 : 1
• This means: Liquid A = (4/5) × x, Liquid B = (1/5) × x

Step 2: 45 litres of the mixture is removed

• The removed 45 litres will also be in the ratio 4:1
• So removed A = (4/5) × 45 = 36 litres
• Removed B = (1/5) × 45 = 9 litres

Step 3: Update the remaining quantities

• Remaining A = (4/5) × x - 36
• Remaining B = (1/5) × x - 9
• Then 45 litres of B is added
• New B = (1/5) × x - 9 + 45 = (1/5)x + 36

Step 4: Use the new ratio A : B = 2 : 5

((4/5)x - 36) / ((1/5)x + 36) = 2 / 5

Cross-multiply:
5 × ((4/5)x - 36) = 2 × ((1/5)x + 36)

⇒ 4x - 180 = (2/5)x + 72

Now simplify:
4x - (2/5)x = 72 + 180
(20x - 2x)/5 = 252
18x / 5 = 252
⇒ 18x = 1260
⇒ x = 70

Answer: 70 litres

The total capacity of the tin is 70 litres.

This question demonstrates a key application of ratio and replacement concepts in quantitative aptitude. It challenges the ability to track changes in proportion through replacement and recalculation, a vital skill in many exams and real-world scenarios.