CAT Concept of successive change - Practice Questions & MCQ

A concept of successive change relates to the calculation of changes in a particular value over a consecutive period of time. It involves understanding how a certain quantity has increased or decreased in percentage terms over a series of steps or iterations.

Understanding Percentage Increase/Decrease

Percentage increase or decrease can be calculated using the formula:

Percentage Change = (Final Value - Initial Value) / Initial Value * 100. 

This formula helps us determine the percentage change between two values.

Applications of Successive Change Concept

The concept of successive change finds applications in various fields such as finance, economics, and business management. It is particularly crucial for analyzing trends, growth rates, and making projections based on past data.

Example 1: Percentage Increase

Let's consider a scenario where the sales of a company have increased from Rs. 50,000 in 2018 to Rs. 60,000 in 2019, and further to Rs. 75,000 in 2020. We can find the percentage increase in sales for each year as follows: 

2019: Percentage Increase = ((60,000 - 50,000) / 50,000) * 100 = 20% 

2020: Percentage Increase = ((75,000 - 60,000) / 60,000) * 100 = 25%

Example 2: Percentage Decrease

Suppose the population of a town was 10,000 in 2015, 8,000 in 2016, and 6,000 in 2017. The percentage decrease in population for each year can be calculated as: 

2016: Percentage Decrease = ((8,000 - 10,000) / 10,000) * 100 = -20% 

2017: Percentage Decrease = ((6,000 - 8,000) / 8,000) * 100 = -25%

Tips and Tricks for Calculating Successive Changes:

- When dealing with successive increases or decreases, always consider the initial base value for calculations. 

- To calculate the total cumulative percentage change, add up the individual percentage changes. 

- It is essential to be attentive while interpreting negative percentage changes. A negative percentage indicates a decrease, whereas a positive percentage indicates an increase.

Solved Examples:

Question 1: The price of a product increased by 20% in the first week, then decreased by 15% in the second week. What is the net percentage change in the price of the product over two weeks? 

Solution: 

Percentage Increase in the first week = 20% 

Percentage Decrease in the second week = 15% 

Net Percentage Change = (20 - 15) / (1 + (20/100)) * (1 - (15/100)) * 100 = 4.55% 

Question 2: The population of a city was 1,20,000. It increased by 8% in the first year and decreased by 10% in the second year. Find the population after two years.

Solution: 

Population after the first year = 1,20,000 + (8/100) * 1,20,000 = 1,29,600 

Population after the second year = 1,29,600 - (10/100) * 1,29,600 = 1,16,640 Therefore, the population after two years is 1,16,640. 

These examples and solutions highlight the practical usage of the concept of successive change for solving problems in management entrance exams. Understanding this concept can significantly help in tackling related questions efficiently.