Following table provides figures (in rupees) on annual expenditure of a firm for two years - 2010
and 2011.
Category 2010 2011
Raw material 5200 6240
Power & fuel 7000 9450
Salary & wages 9000 12600
Plant & machinery 20000 25000
Advertising 15000 19500
Research & Development 22000 26400
In 2011, which of the following two categories have registered increase by same percentage?
Options:
(A) Raw material and Salary & wages
(B) Salary & wages and Advertising
(C) Power & fuel and Advertising
(D) Raw material and Research & Development
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2013 Q.63)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Statistical Physics & Thermodynamics** within *Section 5: Thermodynamics and Statistical Physics* (2 Marks, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Statistical Physics & Thermodynamics:
- Applying canonical quantum/electrodynamic equations:
$\hat{H}\psi = E\psi, \quad \nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}, \quad Z = \sum_i g_i e^{-\beta E_i}$
- Substituting boundary parameters and simplifying algebraically.
- The resulting expression uniquely corresponds to Option **(B)**.
**3. Final Answer**:
Correct Option is **(B)**.
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