To solve this problem, we'll work step by step, calculating how the volume changes after each modification:

1. Initial Reduction:

   • The balloon's volume decreases by 60%.
   • If the original volume is $V$, after a 60% decrease, the remaining volume is: $V_{\text{reduced}} = V \times (1 - 0.60) = V \times 0.40$ So, the volume is now 40% of the original.

2. Subsequent Increase:

   • The reduced volume is then increased by 50%.
   • This means the new volume becomes: $V_{\text{new}} = V_{\text{reduced}} \times (1 + 0.50) = V \times 0.40 \times 1.50 = V \times 0.60$ The new volume is 60% of the original volume.

3. Percentage Change in Volume:

   • Initially, the volume was $V$, and the final volume is $0.60V$.
   • The change in volume is therefore: $\text{Change in Volume} = V_{\text{new}} - V = 0.60V - V = -0.40V$
   • The percentage change in volume is: $\text{Percentage Change} = \frac{\text{Change in Volume}}{V} \times 100\% = \frac{-0.40V}{V} \times 100\% = -40\%$

So, the volume of the balloon ultimately decreases by 40%.

Would you like any further details on this solution or have any other questions?

Related Questions:

1. How would the percentage change differ if the initial decrease were 70%?
2. What happens if the percentage decrease and increase are the same?
3. How do you calculate the percentage change if there are multiple stages of increase and decrease?
4. What is the effect of a 100% increase after a 60% decrease?
5. How can this approach be applied to other properties like area or length?

Tip: When dealing with percentage changes in sequence, always apply each change to the current value, not the original.