Step 1: Standard Limits in Drinking Water:
According to international standards (like WHO or BIS) for drinking water:
- Maximum limit for Copper (Cu) = \( 3.0 \, \text{ppm} \) (or \( \text{mg/L} \)). (Note: Some older texts say 3 ppm, NCERT mentions 3 ppm). Wait, let's verify with standard NCERT Environmental Chemistry data.
NCERT Table values:
- Copper (Cu): 3.0 mg/L (ppm)
- Zinc (Zn): 5.0 mg/L (ppm)
Let's verify the "x" relation.
Given Cu limit = \( x = 3.0 \).
Zn limit is 5.0.
We need to express 5.0 in terms of \( x \) (where \( x=3 \)).
\( \text{Zn limit} = k \cdot x \implies 5 = k \cdot 3 \implies k = 5/3 = 1.66 \).
None of the options match \( 1.66x \).
Let's re-check the standard limits in typical exams (JEE/NEET often use specific values):
Sometimes Cu is given as 2.0 ppm or Zinc as 3.0 ppm? No.
Let's check alternative standard values:
US EPA: Cu = 1.3 ppm, Zn = 5 ppm.
WHO: Cu = 2 ppm, Zn = 3 ppm?
Let's check the relation based on options.
If \( x \) (Cu) is 3 ppm and Zn is 5 ppm: \( 5 \approx 1.5 \times 3 \) (4.5 vs 5). Close to Option A.
If \( x \) (Cu) is 2 ppm and Zn is 3 ppm? No.
Let's look at the options mathematically:
(1) 1.5x
(2) x/1.5
(3) 0.6x
(4) 5/6 x
Let's assume the question refers to a specific dataset where:
Cu = 2.0 ppm.
Zn = 3.0 ppm? No.
Standard NCERT: Fe=0.2, Mn=0.05, Al=0.2, Cu=3.0, Zn=5.0, Cd=0.005.
If \( x=3 \) and Zn limit is 5.
\( 5/3 x = 1.67 x \).
Maybe the Cu limit is considered 2.0 ppm (WHO guideline) and Zn is 3.0 ppm (aesthetic limit)? Then \( 3 = 1.5 \times 2 \). This fits exactly \( 1.5x \).
Or Cu = 3 ppm, Zn = 4.5 ppm?
Option (A) is the only one>x. Zn is allowed in higher concentrations than Cu. Options C and D imply Zn limit<Cu limit, which is false (Zn is much less toxic). Option B implies Zn<Cu.
Thus, logical reasoning: Zn limit>Cu limit. Only Option (A) satisfies this condition.
Step 2: Conclusion:
Since Zinc is less toxic than Copper, its permissible limit is higher. \( \text{Limit}_{Zn}>\text{Limit}_{Cu} \).
\( \text{Limit}_{Zn}>x \).
Only option (A) \( 1.5x \) is greater than \( x \).