P invested ₹ 5000 per month for 6 months of a year and Q invested ₹ x per
month for 8 months of the year in a partnership business. The profit is shared in
proportion to the total investment made in that year.
If at the end of that investment year, Q receives
ସ
ଽ of the total profit, what is the
value of x (in ₹)?
Options:
(A) 2500
(B) 3000
(C) 4687
(D) 8437
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2022 Q.7)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Quantitative & Analytical Aptitude** within *General Aptitude* (2 Marks, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Quantitative & Analytical Aptitude:
- 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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