Which of the following statements are true ?
30 bags : 18 bags = ₹ 450 : ₹ 270

Answer

To determine whether the statement \(30 \text{ bags} : 18 \text{ bags} = ₹ 450 : ₹ 270\) is true, we will follow these steps:

### Step 1: Identify the ratios
We have two ratios to compare:
- The first ratio is \(30 \text{ bags} : 18 \text{ bags}\)
- The second ratio is \(₹ 450 : ₹ 270\)

### Step 2: Write the ratios in fractional form
We can express the ratios as fractions:
- First ratio: \(\frac{30}{18}\)
- Second ratio: \(\frac{450}{270}\)

### Step 3: Cross-multiply to check for equality
To check if the two ratios are equal, we will cross-multiply:
\[ 30 \times 270 \quad \text{and} \quad 18 \times 450 \]

### Step 4: Calculate the products
Now we will calculate both products:
- For the left-hand side:
\[ 30 \times 270 = 8100 \]
- For the right-hand side:
\[ 18 \times 450 = 8100 \]

### Step 5: Compare the results
Since both products are equal:
\[ 8100 = 8100 \]
This indicates that the two ratios are indeed equal.

### Conclusion
Thus, the statement \(30 \text{ bags} : 18 \text{ bags} = ₹ 450 : ₹ 270\) is **true**.

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