A piece of metal weights 155g in air, 150g is 130g in liquid. The relative density of the metal liquid are respectively

Options

A. 5,5
B. 30,5
C. 31,5
D. 10,15

Explanation

To find the relative density of the metal and the liquid, we will use the following formulas:

1. **Relative Density of a Solid**:
\[ \text{Relative Density (RD) of Solid} = \frac{\text{Weight in Air}}{\text{Weight in Air} - \text{Weight in Water}} \]

2. **Relative Density of a Liquid**:
\[ \text{Relative Density (RD) of Liquid} = \frac{\text{Weight in Air} - \text{Weight in Liquid}}{\text{Weight in Air} - \text{Weight in Water}} \]

### Step 1: Calculate the Relative Density of the Metal (Solid)

**Given:**
- Weight in Air = 155 g
- Weight in Water = 150 g

**Using the formula for relative density of solid:**
\[ \text{RD of Solid} = \frac{155}{155 - 150} \]

**Calculating the denominator:**
\[ 155 - 150 = 5 \]

**Now substituting back:**
\[ \text{RD of Solid} = \frac{155}{5} = 31 \]

### Step 2: Calculate the Relative Density of the Liquid

**Given:**
- Weight in Liquid = 130 g

**Using the formula for relative density of liquid:**
\[ \text{RD of Liquid} = \frac{155 - 130}{155 - 150} \]

**Calculating the numerator:**
\[ 155 - 130 = 25 \]

**Using the previously calculated denominator:**
\[ 155 - 150 = 5 \]

**Now substituting back:**
\[ \text{RD of Liquid} = \frac{25}{5} = 5 \]

### Final Answers
- Relative Density of the Metal (Solid) = 31
- Relative Density of the Liquid = 5

### Summary
The relative densities are:
- Metal: 31
- Liquid: 5