The percentage of metals in a mine of lead ore is 60%. Now the percentage of silver is `3/4`% of metals and the rest is lead. If the mass of ore extracted from this mine is 8000 kg, the mass (in kg.) of lead is:

Options

A. 4763
B. 4762
C. 4764
D. 4761

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the mass of metals in the ore.
Given that the percentage of metals in the lead ore is 60%, we can find the mass of metals in the 8000 kg of ore.

\[ \text{Mass of metals} = \text{Total mass of ore} \times \frac{\text{Percentage of metals}}{100} \]

Substituting the values:

\[ \text{Mass of metals} = 8000 \times \frac{60}{100} = 8000 \times 0.6 = 4800 \text{ kg} \]

### Step 2: Calculate the mass of silver.
The percentage of silver is given as \( \frac{3}{4} \% \) of the mass of metals. First, we need to convert \( \frac{3}{4} \% \) into a decimal.

\[ \frac{3}{4} \% = \frac{3}{4} \times \frac{1}{100} = \frac{3}{400} \]

Now, we can calculate the mass of silver:

\[ \text{Mass of silver} = \text{Mass of metals} \times \frac{3}{400} \]

Substituting the mass of metals:

\[ \text{Mass of silver} = 4800 \times \frac{3}{400} = 4800 \times 0.0075 = 36 \text{ kg} \]

### Step 3: Calculate the mass of lead.
The rest of the mass of metals is lead. We can find the mass of lead by subtracting the mass of silver from the mass of metals.

\[ \text{Mass of lead} = \text{Mass of metals} - \text{Mass of silver} \]

Substituting the values:

\[ \text{Mass of lead} = 4800 - 36 = 4764 \text{ kg} \]

### Final Answer:
The mass of lead is **4764 kg**.

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