Quantitative Ability
Faculty Manual 2010
Part I
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Name: __________________________
Centre: ________________________


 

S. No. Title Page No.
1. QA Exercise 1-2: Percentages 1
2. Question Bank: Percentags 9
3. QA Exercise 3-6: Numbers 18
4. Question Bank: Numbers 30
5. QA Exercise 7-8: Ratio 49
6 Question Bank: Ratio 58
7. QA Exercise 9-11: TSD 66
8. Question Bank: TSD 77


QA Faculty Manual 2010
 Page 1
 
Topic: Percentages Lecture Number: 01 Duration: 120 Minutes
Objectives:

Help students to discover what makes the “Percentages” important in almost all the tests.

Help students to learn how to deal with different real-time applications of percentages.

Help students to understand how to go about the study material and what to do before coming to
the next lecture.

Help students to make use of LOGIC in place of conventional methods.
Step 1: Fundamentals - 1
1. Change of base
2. Successive percentage change
Step 2: Fundamentals - 2
3. Simple and compound Interest
4. Interest on interest
5. Formulae for SI and CI
6. Non-annual compounding
Step 3: Class Exercise
Give them sufficient time and discuss few problems from class exercise at the end of the lecture. Tell them
to get the doubts solved with the faculty available at the center before the next lecture.
NOTE: Make necessary announcements.
All the things that are to be discussed in the lecture have been summarized in the
following few pages. Read them carefully and don’t miss anything.
QA Exercise 1 - Percentages: 1
QA Faculty Manual 2010
 Page 2
 
1. A brief Introduction (5-10 mins)
2. Change of base (15 mins)
Start with the simplest problem: If A is 20% more than B, by what percent is B less than A? Do the
same problem if A was 37.5% more than B. Explain why it is important to work with fraction equivalents
to save time & calculations.
Explain that the above simple concept is used extensively even in other topics as follows:
a. if speed increases by 10% over the same distance, by what percent does time decrease?
b. If length of a rectangle decreases by 12.5%, by what percent should its breadth be increased to
maintain the same area?
c. If the volume of a milk and water solution is increased by 25% by pouring just water, by what
percentage does the concentration of milk reduce?
d. If prices decrease by 16.666%, how much percentage can a consumer consume more for the
same amount?
[Q. 2, 6, 8 and 9]
Explain that the above can be used in any relation where M × N = constant.
If prices of apples increase by 25%, I am able to purchase 4 apples less in Rs.80. What was the
original price of one apple? Explain this question orally in the following two methods: Since prices
increased by 25%, I am able to consume 20% less. Thus 20% of original consumption = 4 apples.
Alternately, to maintain consumption i.e. to purchase 4 more apples, I would need 25% of 80 = 16 Rs
more. Thus increased price of apple = Rs. 4 per apple. Now find original price.