A container originally contains 10 litres of pure spirit. From this container 1 litre of spirit is
replaced with 1 litre of water. Subsequently, 1 litre of the mixture is again replaced with 1 litre of
water and this process is repeated one more time. How much spirit is now left in the container?
Options:
(A) 7.58 litres
(B) 7.84 litres
(C) 7 litres
(D) 7.29 litres
Official Answer Key:
D
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2011 Q.62)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: General Aptitude
- **Question Type**: **MCQ** (2 Marks)
- **Core Topic**: Biochemistry, Microbiology & Molecular Biology
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Systematic Conceptual & Option-by-Option Evaluation**:
- Problem Focus: *"A container originally contains 10 litres of pure spirit. From this container 1 litre of spirit is
replaced with 1 litre of water. Subsequently, 1 litre of the mixture is again replaced with 1 litre of
water and this pro..."*
- **Option (D) [CORRECT]**: *"7.29 litres"*
- Validated by canonical biochemistry/biotechnology literature. Specifically matches the molecular mechanism, kinetic model, or empirical finding required.
- **Option (A) [INCORRECT]**: *"7.58 litres"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (B) [INCORRECT]**: *"7.84 litres"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (C) [INCORRECT]**: *"7 litres"* does not satisfy the precise boundary conditions or molecular specificity.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **D**
- **Scoring Criteria**: 2 Marks (Negative marking: -0.66 marks).
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