Percentage

A got 30% of the maximum marks in an examination and failed by 10 marks. However, B who took the same examination got 40% of the total marks and got 15 marks more than the passing marks. What is the pass marks in the examination?

Sol: Let the total marks be 100P. Then as given, 30P + 10 = 40P – 15

Thus, 10P = 25. Thus 100P = 250 {This is total marks.}

Pass marks = 30P + 10 = 75+10 = 85.

Objectives

This Chapter introduces you one of the most important concepts of Quantitative Mathematics, a, nay, the backbone of Quantitative Mathematics. As you will see, this chapter plays a crucial role in developing those calculation skills, required almost in all chapters of Arithmetic but specifically required in many other chapters of Quantitative Mathematics like Time, Speed and Distance; Time and Work; Ratio and Proportion; Time and Work; Profit and Loss; Interpretation of Data, etc.

As you will notice that if you are well-conversant with working out problems of Percentage, you will feel yourself flying on the crest of self-confidence with problems of other chapters too.

In this chapter, I have given a good length of techniques, short-cuts and concept building mechanisms in solving the problems which will take you through all exams.

We start the topic by taking a simple question.

If the cost of a book which is Rs. 40 becomes Rs. 70, what is the percentage increase in the cost?

In fact, through this question, we only want to know that if the original price had been Rs. 100, what would be the extended price. In fact, when we say ‘percentage’, we always mean it with reference to 100. In the present question, what should we do to go from 40 to 100, and correspondingly Rs. 30 will go to our desired value.

It is easy to see that if we multiply 40 by 2.5, we get 100. And we multiply 70 by 2.5, too, and get the value of 175. Hence, there is an increase of Rs. 75 on the base price of Rs. 100. We shall say that percentage increase is 75, or there is an increase of 75%.