### Welcome to Day-4 of the Quantitative Aptitude, Logical Reasoning and Data Interpretation Prep Plan.

#### Focus Topic: Percentage (Arithmetic/Commercial Mathematics)

#### Important Concept for CAT Percentage: Multiplication Factors for Percentage Increase/Decrease

Can you answer the following questions?

• What is the net percentage increase when a number is successively increased by 20% and 30%?

• If the price of an article is increased by 25%, then by what percent it should be reduced to get the same price?

Is the answer in the first case 50% and in the second case 25%? Well that is not the case!!!!

Most competitive examinations are designed in a way that most of the time, we are not required to solve the whole question. The exam is simply concerned about the answer and not steps involved while solving it. In such situations, some simple formulae and tricks can help you solve questions with ease.

One such trick is using multiplication factors for Percentage.

One simple formula that you keep in mind when a quantity N is increased/decreased by S%:

• Increase N by S % = N( 1+ S/100 )

• Decrease N by S % = N (1 – S/100)

For example, a 30% increase in a quantity equals to = Old quantity (1 + 30/100)= 1.3 times old quantity.

Therefore, to find the final quantity after a 30% increase, we multiply the old quantity by a factor of 1.3. Similarly, for a 30% decrease, we multiply the old quantity by 0.7. You can use the multiplication factors given below to find our various percentage increase/decrease are given below:

You can use this table to easily find out subsequent percentage increase/decrease. All you need to do is multiply the corresponding factors and get the final quantity.

**Example:** The salary of a bank employee increases by 10% in the first year, by 20% in the second year, and by 30% in the third year. What is the overall percentage increase in his salary in 3 years?

**Explanation:**Let the initial salary = Rs. 100

To find his salary after 3 years, we simply multiply by the given factors:

Salary after three years= 100 x 1.1 x 1.2 x 1.3 = Rs. 171.6.

Thus, overall percentage increase = 71.6%

This is how you use multiplication tables and simplify life for yourself.

This completes the first lesson we deal with in the QA prep plan. We have covered all the concepts for percentage over the first days. Make sure you have through the two articles for percentage we have featured on an everyday basis.