# Percentage Problems – Part III

The quantitative aptitude section for SBI Clerk, SBI PO, IBPS PO, IBPS Clerk, SSC CGL, SSC CHSL and other competitive exams is sure to have a few questions from the topic percentage. We had earlier discussed what percentage is and what the basic concepts of percentage are.

The most common percentage related questions in bank exams have been classified into 18 easy models. Sometimes, the questions are straight forward where we need to only apply one of these models to find the solution. However, more often than not, we are required to apply two or more of these models to solve the questions based on data interpretation. Which is why understanding each of these concepts and being aware of solving these in “Smart” methods play such an important role when preparing for any bank exam.

The first 5 models have been discussed here . We are now going to understand the next 2 models.

### Model 6: How to find out the percentage change between two values

Percentage change can be either an increase or a decrease. A negative answer implies a decrease and a positive solution implies an increase in the percentage.

Example 1: The profit made by a company in the present year is 15 lakhs. Two years ago, the profit made by the same company was 24 lakhs. What is the percentage change in the profit made by the company?

Solution:

The percentage change in the profit made by this company is -37.5%, which is nothing but a decrease of 37.5% in profit.

### Model 7: Net Percentage change or the Effective Percentage change when there is a percentage change between two other variables Where a and b are the percentage changes in two variables.

This is an important concept which is also used in other topics such as Simple Interest and Compound Interest, Profit and Loss and others.

Example 1: The length of a rectangle increased by 40% and its breadth increased by 20%. What will be the percentage change in the area of the rectangle?

Solution:
By applying the percent change in the formula, we can say that:

Applying the percentage change formula:

And since this is a positive answer, we can say that the change is an increment of 68%.

SMART METHOD:
The same question can be solved in a ‘smart’ method that saves time in competitive exams such as SBI PO exam and SBI Clerk, SBI PO, IBPS PO, IBPS Clerk, SSC CGL, SSC CHSL and other competitive exams. exam since time is of the essence here.

As the length and the breadth increase, so will the area of the rectangle.
If the percentage change in length = a%
And percentage change in breadth = b%

There is a 68% increase in the area.

Similarly, the process would be reversed if the question was altered to:
The length of a rectangle decreased by 40% and its breadth decreased by 20%. What will be the percentage change in the area of the rectangle?

Only here, percentage change in length = -a%
And percentage change in breadth = -b%
Since there is a negative change in both length and breadth:

Since the final result is in negative, it is obvious that the area has decreased by 52%.

Example 2: The revenue of a shop in the month of March was ₨ 40,000. In the month of April, the shopkeeper announced a discount of 20% and hence, his sales went up by 20%. What will be the revenue in the month of April?

Solution:

Hence, the revenue in the month of April has decreased by 4%, when compared to the revenue in the month of March.

Example 3: The price of sugar increased by 25%. What should be the percentage decrease in the consumption of sugar by a family, such that their expenditure on sugar remains the same?

Solution:

Since there is no change in the expenditure, the change between the old expenditure and the new expenditure is 0.

Consumption of sugar must decrease by 20% to keep the expenditure same as before.

Hence, it is easy for us to solve the percentage word problems in bank exams using these smart methods. There are remaining 11 models on percentage. To learn all about them and to understand how to solve each of them in Smart methods, check out our online programs.

For more tips and tricks on calculating percentages for bank exams, sign up for the free mock tests and never stop practising. 