if the speed of a vehicle increased by 100/3% and the time for which it travels decrease by 25% find the percentage increase or decrease in the distance (a) 25/3% increase (b) 25/3% decrease (c) 50/3% increase (d) none of these

Let's analyze the problem step by step.

### Step 1: Define the initial values
- Let the initial speed be \( S \).
- Let the initial time be \( T \).

### Step 2: Calculate the initial distance
- The initial distance \( D_1 \) is given by:
  \[
  D_1 = S \times T
  \]

### Step 3: Determine the new speed and time
- The speed is increased by \( \frac{100}{3} \% \), so the new speed \( S' \) is:
  \[
  S' = S \times \left(1 + \frac{100}{3} \times \frac{1}{100}\right) = S \times \left(1 + \frac{1}{3}\right) = \frac{4S}{3}
  \]
  
- The time is decreased by 25%, so the new time \( T' \) is:
  \[
  T' = T \times \left(1 - \frac{25}{100}\right) = T \times 0.75 = \frac{3T}{4}
  \]

### Step 4: Calculate the new distance
- The new distance \( D_2 \) is given by:
  \[
  D_2 = S' \times T' = \frac{4S}{3} \times \frac{3T}{4} = S \times T = D_1
  \]

### Step 5: Determine the percentage change in distance
Since \( D_2 = D_1 \), there is no change in the distance.

Therefore, the correct answer is:
- **(d) None of these**

Would you like more details or have any questions? Here are 5 related questions you might find interesting:

1. How would the distance change if the speed increased by 50% and the time decreased by 50%?
2. What is the formula for calculating percentage change in general?
3. If the speed and time both increased by 25%, what would be the percentage change in distance?
4. How does the distance traveled relate to speed and time graphically?
5. Can you explain how to solve similar problems using proportional reasoning?

**Tip:** When analyzing problems involving percentage changes, always ensure to apply the percentage change to the correct base quantity to avoid calculation errors.

Learn how to calculate percentage change in distance when the speed of a vehicle increases by 100/3% and the time decreases by 25%. Understand the application of percentage change formula and basic algebra concepts. Suitable for Grades 7-9 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