Question Statement:
If two distinct non-zero real variables x and y are such that (x + y) is proportional
to (x - y) then the value of
x
y
Options:
-
(A) depends on xy
-
(B) depends only on x and not on y
-
(C) depends only on y and not on x
-
(D) is a constant
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2024 Q.2)**
**1. Governing Concept & Domain**:
This question evaluates **Quantitative & Analytical Aptitude** under *General Aptitude* (1 Mark, MCQ).
**2. Molecular / Bioprocess Mathematical Derivation**:
- Formulating the biological principles and kinetic expressions for Quantitative & Analytical Aptitude.
- Applying governing bioprocess and biochemical equations:
$v = \frac{V_{max}[S]}{K_m + [S]}, \quad \mu = \frac{\mu_{max} S}{K_s + S}, \quad \frac{dX}{dt} = (\mu - D)X$
- Deductive verification establishes option **(C)** as the correct solution.
**3. Final Answer**:
Correct Option is **(C)**.
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