Check whether the following numbers are in proportion or not :
30, 40, 45, 60

Answer

To check whether the numbers 30, 40, 45, and 60 are in proportion, we need to compare the ratios of the first two numbers with the ratios of the last two numbers. Here’s how we can do this step by step:

### Step 1: Write the ratios
We need to find the ratio of the first pair (30 and 40) and the second pair (45 and 60).

**Ratio of the first pair:**
\[ \text{Ratio of } 30 \text{ and } 40 = \frac{30}{40} \]

**Ratio of the second pair:**
\[ \text{Ratio of } 45 \text{ and } 60 = \frac{45}{60} \]

### Step 2: Simplify the ratios
Now, we simplify both ratios.

**Simplifying the first ratio:**
\[ \frac{30}{40} = \frac{3}{4} \quad (\text{Divide both numerator and denominator by 10}) \]

**Simplifying the second ratio:**
\[ \frac{45}{60} = \frac{3}{4} \quad (\text{Divide both numerator and denominator by 15}) \]

### Step 3: Compare the simplified ratios
Now we compare the simplified ratios:
- The first ratio is \( \frac{3}{4} \)
- The second ratio is also \( \frac{3}{4} \)

Since both ratios are equal, we can conclude that the numbers are in proportion.

### Conclusion
The numbers 30, 40, 45, and 60 are in proportion because:
\[ \frac{30}{40} = \frac{45}{60} \]