Methods to Solve Percentages Related Questions

The problems related to the percentages are a part of the quantitative analysis section of the CAT examination. There are at least 1 or 2 questions asked regarding this type every year. This topic in itself is really simple and scoring as well. Besides, the advantages of this topic do not limit just to the percentages. They play a much greater role in the concept of profit, loss and interests. By making use of the formulas to find out percentages, we can effectively use the values for many other mathematical functions.

How to Solve CAT Percentage Questions?

To be able to solve percentage proves in the CAT examination, you need to have a firm understanding of the topic of percentages. You need to be able to calculate the percentages of numbers very quickly. Also, the representation of the percentages in the form of fractions is advantageous in these types of questions.  

Firstly, use all the given data to find the actual percentage of a quantity that has been put into effect. Take into account if the quantity has a percentage increase or percentage decrease in it and use the related formula. However, there are certain sets of tricks and formulas that can be helpful to you. Nothing will serve you better than your wisdom. 

You should be acquainted with the mathematical operations of multiplication and division. Also, the basic understanding of the concept of squares and cube roots in the problems related to percentages is helpful. Besides all that, try to remember the formulas for all the important topics that are related to the concept of percentages. 

These percentage questions can be asked regarding any finite quantity or in the form of some variables. Also, calculations of simple interest, compound interest, profit and loss, and percentage increase or decrease are very important parts of this topic of percentages. 

Practice Questions on Percentage for CAT

1. A fruit seller had some apples. He sells 30% apples and still has 390 apples. How many apples did he originally have?
2. For the percentage of two-digit numbers that end with either 1 or 9.
3. There has been an increase of 13% in the worth of an object. But after some time its worth decreased by 17%. What is the percentage change of the worth of the object?
4. In percentages, how will the fraction ⅞ represent as?
5. What will be the 17% of 1700?
6. What will be the new value of an object after it has been increased by 23%?

Solved Examples of Percentages Related Questions for CAT Exams

In a class of 60 students, 20% are male. 65% of female students passed an exam conducted for the whole class. What is the number of female students who passed the exam?

From the statement, it can be concluded that the class has 20% boys and 80% girls. 

The total number of girls in 60 students ts will be given by:

(80 / 100) × 60 = 48

Now of those, only 65% have passed;

Number of girls that have passed = 

65% of 48 ≈ 31

Close to 31 girls have passed the examination.

Evaluate the given problem: 33.33% of 99 + 81.81% of 495

The 33.33% of 99 can be given as 1 / 3 of 99;

= 33

Now, 81.81% of 495 is;

≈ 405.

Hence, the solution to the problem will be given as;

= 33 + 405

= 438.

What will the change be in yeh quantity of an object, if its size is reduced by 30% after it has already been increased by 30?

Let the original size of the object be x units. 

Firstly, taking into account the phenomenon of percentage increase;

The size of the object has become by a measure of (3x / 10)

The new value for the size of the object is x + (3x / 10)

= 13x / 10

Now decreasing 30% from this new value;

(13x / 10) × 7 / 10

= 9x / 10.

This will account for the 9% decrease in the actual size of the object. 

Conclusion

The concept of percentages gives us a clear understanding of the amount of change that has been brought in a value after any operation. The operations related to this process can be mathematical operations, increase or decrease in the values, or interest accumulated. Making use of these calculations, we can easily relate two entities to each other. Also, it is to be noted that the topic of percentages makes up the very basis of many other mathematical concepts. By gaining a good understanding of percentages, we can get an understanding of many other topics as well.