Wednesday, March 16, 2016

Short Tricks On Averages

For Downloadable PDF format on Short Tricks on Average click here

Average

1 What is Average?
A calculated "central" value of a set of numbers.

Average =          Sum of Observation
                         Number of Observation

When we cross multiply
Sum of observation = Average of Observations * Number of observation
           
2 In case of Average speed, the formula will change

What is Average Speed?

Average Speed is the total distance traveled by an objects divided by total time taken.

If distance and time are not mentioned rather the speeds are given, then;

Suppose a man covers a certain distance at X km/h and an equal distance at Y km/h
Then the Average Speed during the whole journey is

Average Speed =   2XY
                              X+Y

When there are three speeds X km/h, Y km/h & Z km/h

Average Speed =   3XYZ
                             XY+YZ +ZX

For Better Understanding Click here.

3. If the average of n1 items is p1 and the average of n2 items is p2 then
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The average of total items will be

n1p1 + n2p2  
    n1 +n2

Example: There are 60 students in a class. Out of which 40 are boys and 20 are girls. If the average age of boys is 15 years and that of girls is 16 years then find the average age of the class.
40*15 + 20*16.
          60
Ans. 15.33 years

4. When we have to find the average of consecutive odd numbers

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Then,

Case 1: - When the number of observation is Even

Example: - 11, 13, 15, 17 (here the number of observation is 4, even)

Divide the numbers equally in two parts
11, 13 …….15, 17

The number between middle two terms is average, i.e. 14 in this case.

Alternative method: Sum of extremes divided by 2
Here 11+17 = 14
                2

Case 2: - When the number of observation is Odd

Example: - 163, 165, 167,169,171 (here the number of observation is 5, Odd)

Here the middle term is the average i.e. 167

For Better Understanding click here.

5. Average of consecutive first n natural numbers is

    n+1    .
      2
Average of first 20 natural numbers is 20+1 divided by 2 i.e. 10.5.

Sum of first consecutive n natural numbers is

n(n+1)  .
    2
As

Sum of Observations = Average of Observations * Number of observation

6. Average of consecutive first n natural even numbers is n+1.

Example: - Average of consecutive first 5 natural even numbers is 5+1 =6

Long method      2+4+6+8+10
                                              5
30/5= 6

Average of consecutive first n natural odd numbers is n.

Example: - Average of consecutive first 5 natural odd numbers is 5

Long method      1+3+5+7+9
                                              5
25/5= 5

For Better Understanding click here.

Average of n multiples of p will be
 
    p(n+1)  .
         2

Example: Average of 3 multiples of 5 is

5(3+1)/2 =
Long method 5+10+15
                                    2
Ans. 10

For Better Understanding click here.

Saturday, February 13, 2016

Ratio and Proportion

For downloadable notes in PDF format click here :- Concept of Ratio And Proportion


     What is RATIO?

The ratio of two quantities a and b in the same units, is the fraction a/b and we write it as a: b.

In the ratio a: b, we call a as the first term or antecedent and b, the second term or consequent.

Ex. The ratio 6:8 represents 6/8 with antecedent = 6, consequent =8

Rule: The multiplication or division of each term of a ratio by the same non-zero number does not affect the ratio.

Ex.  3: 4 = 6: 8 = 12: 16 etc.

For Better Understanding click here.

    2. What is PROPORTION?

The equality of two ratios is called proportion.

If a: b = c: d, we write, a: b: c: d and we say that a, b, c, d are in proportion.

 Here a and d are called extremes, while b and c are called mean terms.

 Product of means = Product of extremes.

Thus, a: b: c: d <=> (b x c) = (a x d).

3. (i) Fourth Proportional: If a : b = c: d, then d is called the fourth proportional
            to a, b, c.
   (ii) Third Proportional: If a: b = b: c, then c is called the third proportional to
            a and b.
   (iii) Mean Proportional: Mean proportional between a and b is square root of ab

4. (i) COMPARISON OF RATIOS:

        We say that (a: b) > (c: d) <=>  (a/b)>(c /d).

      (ii) COMPOUNDED RATIO:

            The compounded ratio of the ratios (a: b), (c: d), (e : f) is (ace: bdf)

For Better Understanding click here.

5. (i) Duplicate ratio of (a : b) is (a2 : b2).
      (ii) Sub-duplicate ratio of (a : b) is (a : b).
     (iii)Triplicate ratio of (a : b) is (a3 : b3).
     (iv) Sub-triplicate ratio of (a : b) is (a : b ).
     (v) If (a/b)=(c/d), then  ((a+b)/(a-b))=((c+d)/(c-d))    (Componendo and dividendo)

For Better Understanding click here.




Verbal Ability

  • Vocabulary Based (Synonyms Antonyms)
  • English Usage or Grammar
  • Sentence Correction
  • Fill in the blanks
  • Cloze Passage
  • Analogies or Reverse Analogies
  • Jumbled Paragraph
  • Meaning-Usage Match
  • Summary Questions
  • Verbal Reasoning
  • Facts / Inferences / Judgements
  • Reading Comprehension

Logical Reasoning

  1. Number and Letter Series
  2. Calendars
  3. Clocks
  4. Cubes
  5. Venn Diagrams
  6. Binary Logic
  7. Seating Arrangement
  8. Logical Sequence
  9. Logical Matching
  10. Logical Connectives
  11. Syllogism
  12. Blood Relations

Data Interpretation

  1. Tables
  2. Column Graphs
  3. Bar Graphs
  4. Line Charts
  5. Pie Chart
  6. Venn Diagrams
  7. Caselets
Combination of two or more types linked to each other.

Quantitative Ability

  1. Number Systems
  2. LCM and HCF
  3. Percentages
  4. Profit, Loss and Discount
  5. Interest (Simple and Compound)
  6. Speed, Time and Distance
  7. Time and Work
  8. Averages
  9. Ratio and Proportion
  10. Linear Equations
  11. Quadratic Equations
  12. Complex Numbers
  13. Logarithm
  14. Progressions (Sequences & Series)
  15. Binomial Theorem
  16. Surds and Indices
  17. Inequalities
  18. Permutation and Combination
  19. Probability
  20. Functions
  21. Set Theory
  22. Mixtures and Alligations
  23. Geometry
  24. Co-ordinate Geometry
  25. Trigonometry
  26. Mensuration