https://file.aiquickdraw.com/mathbot/file/17231234805014xhazcog.jpg

https://file.aiquickdraw.com/mathbot/file/1723123480502i9bpljyf.jpg

I see you've uploaded an image with handwritten mathematical problems. I'll extract the text and provide solutions to each problem.

### Extracted Problems:

1. **Q1:** If the fare of a taxi is increased by 20%, the old price being $10, it is observed that the number of trips fell by 15%. Then, the price elasticity of demand is _______.

2. **Q2:** An industry charges $ P_1 $ for sitting at home. If there is a labor strike, it charges $ P_2 $. 50% of charges are labor costs. Find $ \frac{P_1}{P_2} $.

3. **Q3:** Out of 800 oranges, 560 are found rotten. Find the percentage of good oranges.

4. **Q4:** A student requires 35% marks to qualify in the examination. If he secured 188 marks and failed by 62 marks, find the total marks.

5. **Q5:** Find $ x $ if 35% of $ x $ is 525.

### Solutions:

**Q1:** 
The price elasticity of demand (PED) is calculated using the formula:
\[
\text{PED} = \frac{\% \text{Change in Quantity Demanded}}{\% \text{Change in Price}}
\]
Here, the price is increased by 20%, and the demand (number of trips) decreased by 15%. So,
\[
\text{PED} = \frac{-15\%}{20\%} = -0.75
\]
**Answer:** The price elasticity of demand is $-0.75$.

---

**Q2:**
Let $ C $ be the total cost, and 50% of it is labor cost. 
So, $ C = P_1 + P_2 $ and $ C = 2 \times \text{Labor Cost} = 2 \times \frac{C}{2} = P_1 + P_2 $.

Since the charges are due to labor costs and the problem states $ \frac{P_1}{P_2} $,
The relationship would be:
\[
\frac{P_1}{P_2} = 1
\]
This implies that $ P_1 = P_2 $ under these conditions.

**Answer:** $ \frac{P_1}{P_2} = 1 $.

---

**Q3:** 
Total oranges = 800, Rotten oranges = 560.
Good oranges = $ 800 - 560 = 240 $.
Percentage of good oranges:
\[
\frac{240}{800} \times 100 = 30\%
\]
**Answer:** 30% of the oranges are good.

---

**Q4:** 
The student scored 188 marks and failed by 62 marks. So, the required marks to pass are $ 188 + 62 = 250 $.
Since 35% of the total marks is 250, let the total marks be $ x $.
\[
0.35x = 250
\]
\[
x = \frac{250}{0.35} = 714.29 \approx 714
\]
**Answer:** The total marks are 714.

---

**Q5:** 
$ 0.35x = 525 $
\[
x = \frac{525}{0.35} = 1500
\]
**Answer:** $ x = 1500 $.

---

Would you like further details on any of these solutions or explanations?

---

### Related Questions:
1. How is price elasticity of demand interpreted when it is negative?
2. What factors could affect the price elasticity of demand in real-world scenarios?
3. How are labor costs typically calculated in production costs?
4. Can you explain other types of elasticity in economics, such as income elasticity?
5. How can the percentage of good items be used in quality control?
6. What methods can be used to pass an exam with minimum marks?
7. How does rounding affect the final answer in percentage problems?
8. How are labor strikes typically resolved in economic models?

---

**Tip:** In percentage problems, always ensure the percentage is correctly converted into its decimal form before performing calculations.

Explore detailed solutions to price elasticity of demand problems and percentage calculations. Learn how to calculate price elasticity of demand and solve percentage problems step-by-step. Suitable for advanced high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation