A mixture of cement, sand and gravel in the ratio of 1 : 2 : 4 by volume is required. A person wishes to measure out quantities by weight. He finds that the weight of one cubic foot of cement is 94 kg, of sand 100 kg and gravel 110 kg. What should be the ratio of cement, sand and gravel by weight in order to give a proper mixture?
(a)`47 : 100 : 220`
(b)` 94 : 100 : 220`
(c)` 47 : 200 : 440`
(d)None of these

Options

A. `47 : 100 : 220`
B. ` 94 : 100 : 220`
C. ` 47 : 200 : 440`
D. None of these

Answer

To solve the problem, we need to convert the given volume ratio of cement, sand, and gravel into a weight ratio using the weights of each material per cubic foot.

### Step-by-Step Solution:

1. **Identify the Volume Ratio**:
The volume ratio of cement, sand, and gravel is given as:
\[ \text{Cement} : \text{Sand} : \text{Gravel} = 1 : 2 : 4 \]

2. **Weights of Each Material**:
The weights of 1 cubic foot of each material are provided as:
- Cement = 94 kg
- Sand = 100 kg
- Gravel = 110 kg

3. **Calculate the Weight for Each Material**:
We will multiply the volume ratio by the respective weights to find the total weight for each material:
- For Cement:
\[ \text{Weight of Cement} = 1 \times 94 = 94 \text{ kg} \]
- For Sand:
\[ \text{Weight of Sand} = 2 \times 100 = 200 \text{ kg} \]
- For Gravel:
\[ \text{Weight of Gravel} = 4 \times 110 = 440 \text{ kg} \]

4. **Combine the Weights**:
Now we have the weights:
\[ \text{Cement} : \text{Sand} : \text{Gravel} = 94 : 200 : 440 \]

5. **Simplify the Ratio**:
To simplify the ratio, we can divide each term by 2:
\[ \frac{94}{2} : \frac{200}{2} : \frac{440}{2} = 47 : 100 : 220 \]

6. **Final Ratio**:
The final weight ratio of cement, sand, and gravel is:
\[ 47 : 100 : 220 \]

### Conclusion:
The correct answer is option (a) `47 : 100 : 220`.