Short Answer

Successive percentage changes are calculated when a value changes more than once. Each change is applied step by step on the updated value, not on the original value. This means the second change is based on the new value after the first change.

For example, if a value increases by 10% and then again by 20%, we first increase it by 10%, and then apply 20% on the new value. This method gives the correct final result.

Detailed Explanation:

Successive percentage changes calculation

Successive percentage changes mean applying more than one percentage change one after another on a value. These changes can be increases, decreases, or a combination of both. The important point is that each change is applied to the new value obtained after the previous change.

This is different from adding percentages directly. Many people think that if a value increases by 10% and then 20%, the total increase is 30%, but this is not correct. Each percentage change works on the updated value, so we must calculate step by step.

Basic concept of successive change

In successive percentage changes, the first percentage change is applied to the original value. Then, the second percentage change is applied to the new value obtained after the first change. This process continues for all changes.

For example, if a price is 100 and it increases by 10%, the new value becomes 110. Then, if it increases again by 20%, we calculate 20% of 110, not 100. So, the increase is 22, and the final value becomes 132.

Formula for successive changes

There is a shortcut formula for successive percentage changes:

Here, “a” and “b” are the two percentage changes. This formula works when both changes are increases. If one is decrease, we take it as negative.

For example, if there is a 10% increase followed by 20% increase, then:

So, the total increase is 32%, not 30%.

Types of successive changes

Successive percentage changes can be of different types depending on the situation. They can be two increases, two decreases, or one increase followed by one decrease.

Two successive increases

When both changes are increases, we use the formula directly. For example, 15% increase followed by 10% increase gives:

Two successive decreases

When both changes are decreases, we use the same formula but consider both as negative. For example, 10% decrease followed by 20% decrease gives:

So, the net decrease is 28%.

One increase and one decrease

When one change is increase and the other is decrease, we treat decrease as negative. For example, 20% increase followed by 10% decrease:

So, the net increase is 8%.

Step by step method

Another method is to apply each percentage one by one. For example, if a value is 200 and increases by 10% and then decreases by 5%, we first increase 200 by 10% to get 220. Then we decrease 220 by 5%, which is 11. So, the final value becomes 209.

Importance in real life

Successive percentage changes are used in many real-life situations such as price changes, salary adjustments, profit and loss, and population growth. It helps in finding the correct final value after multiple changes.

Common mistakes

A common mistake is simply adding percentages without considering their effect on updated values. This gives wrong results. So, it is important to apply each percentage change step by step or use the correct formula.

Conclusion

Successive percentage changes are calculated by applying each change on the updated value. Using the correct method or formula helps in finding accurate results in practical situations.