A certain metal M ocas in four compounds namely A,B,C and D. A has 20% of M, B has 68% of M, C has 73% of M and D has 60% of M. If metal M is extracted from A,B,C and D, it costs Rs 35 per kg, Rs 40 per kg, Rs 100 per kg and Rs 45 per kg respectively. which mineral can be considered as an effective ore of M?

Options

A. A
B. B
C. C
D. D

Answer

To determine which mineral can be considered as an effective ore of metal M, we need to analyze the percentage of metal M in each compound (A, B, C, and D) and the cost of extracting 1 kg of metal M from each compound.

### Step-by-Step Solution:

1. **Identify the Percentage of Metal M in Each Compound**:
- Compound A: 20% of M
- Compound B: 68% of M
- Compound C: 73% of M
- Compound D: 60% of M

2. **Calculate the Amount of Each Compound Required to Extract 1 kg of Metal M**:
- For compound A:
\[ 20\% \text{ of } X_A = 1 \text{ kg} \implies \frac{20}{100} \times X_A = 1 \implies X_A = \frac{1 \times 100}{20} = 5 \text{ kg} \]
- For compound B:
\[ 68\% \text{ of } X_B = 1 \text{ kg} \implies \frac{68}{100} \times X_B = 1 \implies X_B = \frac{1 \times 100}{68} \approx 1.47 \text{ kg} \]
- For compound C:
\[ 73\% \text{ of } X_C = 1 \text{ kg} \implies \frac{73}{100} \times X_C = 1 \implies X_C = \frac{1 \times 100}{73} \approx 1.36 \text{ kg} \]
- For compound D:
\[ 60\% \text{ of } X_D = 1 \text{ kg} \implies \frac{60}{100} \times X_D = 1 \implies X_D = \frac{1 \times 100}{60} \approx 1.67 \text{ kg} \]

3. **Calculate the Cost of Extracting 1 kg of Metal M from Each Compound**:
- Cost from compound A:
\[ \text{Cost}_A = X_A \times \text{Cost per kg} = 5 \text{ kg} \times 35 \text{ Rs/kg} = 175 \text{ Rs} \]
- Cost from compound B:
\[ \text{Cost}_B = X_B \times \text{Cost per kg} = 1.47 \text{ kg} \times 40 \text{ Rs/kg} \approx 58.8 \text{ Rs} \]
- Cost from compound C:
\[ \text{Cost}_C = X_C \times \text{Cost per kg} = 1.36 \text{ kg} \times 100 \text{ Rs/kg} = 136 \text{ Rs} \]
- Cost from compound D:
\[ \text{Cost}_D = X_D \times \text{Cost per kg} = 1.67 \text{ kg} \times 45 \text{ Rs/kg} \approx 75.15 \text{ Rs} \]

4. **Compare the Costs**:
- Cost of extracting 1 kg of M:
- From A: 175 Rs
- From B: 58.8 Rs
- From C: 136 Rs
- From D: 75.15 Rs

5. **Determine the Most Effective Ore**:
- The compound with the lowest cost for extracting 1 kg of metal M is compound B, costing approximately 58.8 Rs. Therefore, compound B can be considered the most effective ore of metal M.

### Conclusion:
The mineral that can be considered as an effective ore of metal M is **compound B**.