Step-by-step explanation:
Let's solve each part step by step:
**(a) Increase 180 in the ratio 6:9**
To increase 180 in the ratio 6:9 means we need to find the equivalent increase in the same ratio.
1. **Find the total parts in the ratio 6:9**:
Total parts = 6 + 9 = 15
2. **Calculate the increase factor**:
Increase factor = 180 / 6 = 30
3. **Calculate the increase for each part**:
Increase per part = Increase factor * 9 (since 9 is the part that corresponds to the increase)
Increase per part = 30 * 9 = 270