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The question extracted from the image is as follows:

**The increase in the price of a certain item was 25%. Then the price was decreased by 20% and then again increased by 10%. What is the resultant increase in the price?**

Options:
- (a) 5%
- (b) 10%
- (c) 12.5%
- (d) 15%

### Solution:

Let the original price of the item be \( P \).

1. **First increase by 25%**:  
   New price = \( P + 25\% \times P = P(1 + 0.25) = 1.25P \)

2. **Next, a decrease of 20% on the new price**:  
   New price = \( 1.25P - 20\% \times 1.25P = 1.25P \times (1 - 0.20) = 1.25P \times 0.80 = 1.00P \)  
   Now the price is back to \( P \).

3. **Finally, an increase of 10%**:  
   New price = \( 1.00P + 10\% \times 1.00P = P \times (1 + 0.10) = 1.10P \)

Thus, the resultant price is \( 1.10P \), which is an overall increase of **10%** from the original price.

The correct answer is **(b) 10%**.

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Would you like more details or have any questions? 

Here are 5 related questions you could explore:

1. What happens if the order of the price changes is reversed?
2. How do you calculate the net percentage change in a series of percentage increases and decreases?
3. What is the general formula for calculating successive percentage changes?
4. How can we use logarithms to solve complex percentage increase and decrease problems?
5. How does compounding affect percentage-based price changes?

**Tip:** Successive percentage increases and decreases don't simply add up. They multiply, which is why calculations are a bit more involved.

The increase in the price of a certain item was 25%. Then the price was decreased by 20% and then again increased by 10%. What is the resultant increase in the price?

This problem involves calculating successive percentage changes where an item's price first increases by 25%, decreases by 20%, and then increases again by 10%. It demonstrates how to apply percentage increase and decrease formulas step-by-step.

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