Question Statement:
If
p ∶ q = 1 ∶ 2
q ∶ r = 4 ∶ 3
r ∶ s = 4 ∶ 5
and u is 50% more than s, what is the ratio p ∶ u?
Options:
-
(A) 2 ∶ 15
-
(B) 16 ∶ 15
-
(C) 1: 5
-
(D) 16: 45
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2022 Q.3)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Quantitative & Analytical Aptitude** within *General Aptitude* (1 Mark, 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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