Are the ratio in proportion of weight and volume.
It is given that the weights of 150 litres and 100 litres of kerosene oil are 135 kg and 90 kg respectively.

Answer

To determine if the ratio of weight to volume of kerosene oil is in proportion, we need to compare the ratios of weight and volume for the two given quantities. Here’s the step-by-step solution:

### Step 1: Identify the given quantities
We have:
- Weight of 150 litres of kerosene oil = 135 kg
- Weight of 100 litres of kerosene oil = 90 kg

### Step 2: Write the ratios of weight and volume
We will write the ratios of weight to volume for both quantities.

For 150 litres:
- Ratio of weight to volume = Weight / Volume = 135 kg / 150 litres

For 100 litres:
- Ratio of weight to volume = Weight / Volume = 90 kg / 100 litres

### Step 3: Simplify the ratios
Now, we simplify both ratios.

**For 150 litres:**
\[ \frac{135}{150} = \frac{135 \div 15}{150 \div 15} = \frac{9}{10} \]

**For 100 litres:**
\[ \frac{90}{100} = \frac{90 \div 10}{100 \div 10} = \frac{9}{10} \]

### Step 4: Compare the simplified ratios
Now we compare the two simplified ratios:
- Ratio for 150 litres = 9/10
- Ratio for 100 litres = 9/10

### Step 5: Conclusion
Since both ratios are equal (9/10 = 9/10), we can conclude that the ratios of weight to volume are in proportion.

### Final Answer
Yes, the ratio of weight and volume of kerosene oil is in proportion.

---