Contents of Chapters
- Tables
- Line Graph
- Bar Graph
- Pie Charts (or Circle Graphs)
- Venn Diagram
==>> Follow Data Interpretation Guide
Techniques for Ratio
Eg 1. 2/1352 is close to the ratio 1/676
Eg 2. Find the ratio closest to 14.37/241 ?
(a) 3/32 (b) 4/67 (c) 7/11 (d) 5/81
Sol:
Eg. 3. Which is the highest ratio among 13/447,45/508,28/583,18/531?
Sol:
Step 1: Reverse the position of the upper value(numerator) and the lower value(denominator).
Step 2 : Take the closest value
Step 3 : the maximum value is the minimum ratio and minimum value is the maximum ratio.
Eg. 4. Which is the highest ratio among 471/525 , 324/411 , 648/749 ?
Sol:
S1: Approximate the given ratio (if the no. of digits in numerator/denominator is more than 2 )
S2: Multiply the numerator by 10 and get the result fractionS3: Find only the integer value of the result fraction
S4: If any of the integer value of the result fractions is same then find the next decimal places and so on.
S5: Compare the value of the result fractions. The maximum ratio will have maximum value.
Eg 5. Consider , 31/83, 15/46, 22/65, then it is required to find which of the among ratio is less than 1/3 ?
Sol:
Techniques for Percentage
Case 1. To find by how much per cent X is more or less than Y compared to Y.
Example:
ExampleIf A's income is 20% more than B, then how much % B's income is less than that of A's income ?
Sol:
20/120×100
Example
Example
1+10/100=110/100
20/120×100
Case 2. To find the percentage change in any value in year M compared to that value in year K.
The total population of a village is 5000.The number of males and females increases and consequently the population of the village becomes 5600.Find the percentage change in the population?
Sol:
600/5000×100 = 12%
Case 3. To find the original value if the value after its x% increase or decrease is known
Rakesh's salary is increased by 10% and he get now Rs. 5000. Find his salary before the increase ?
Sol:1+10/100=110/100
5000/110×100 = 4545.45
Case 4. Two percentage value cannot be compared unless the base values are known.
Example
6% of income of Ram is equal to 18% of income of Shyam 10% of income of Shyam is equals to 30% of income of Mohan. Find the total income of Ram, Shyam and Mohan ?
Sol:
Cannot be determined.
Case 5. Two percentage values can be compared in terms of percentage values ( but not in absolute values) when the base values are same ( although base values are not known ) .
Example
A's height is 40% less than that of B, how much percent B's height is more than that of A ?
Sol:
Let A = 60 and B = 100
40/60×100 = 662/3%
Case 6. To find the value of a parameter in any year K when the % change in its value over two different periods( any period having the year K) are same.
Example
Techniques for Average
Examples
(1) Find the average annual production increase in product over the period 2000 to 2004 ?
% increase in Production during 2000 - 2004 = 45-25/25×100 = 80%
Average % increase during 2000-04 = 80/5 = 16%
(2) The data of sale of a Company in the different years of its product type x,y,z are as below :
| Year | X | Y | Z | Total |
| 2001 | 8 | 4 | 30 | 42 |
| 2002 | 16 | 16 | 18 | 50 |
| 2003 | 18 | 32 | 24 | 74 |
| 2004 | 14 | 21 | 20 | 55 |
| 2005 | 18 | 16 | 28 | 62 |
(a) In which of the given years the sale of product Z was close to its average sale over the years?
Sol:(30+18+24+20+28) = 120
120/5 = 24
So, the year which is closest to the average is 2003.
(b) In which of the given years the sale of product Z was close to its average sale of all the products in the year ?
Sol:| Year | Average Sale | Sale of Product Z | Difference |
| 2001 | 42/5 = 8.4 | 30 | Difference with average 30-8.4 = 21.6 is very wide, so calculation not required |
| 2002 | 50/5 = 10 | 18 | 18 - 10 = 8 |
| 2003 | 74/5 = 14.8 | 24 | 24-14.8 = 9.2 |
| 2004 | 55/5 = 11 | 20 | 20-11 = 9 |
| 2005 | 62/5 = 12.4 | 28 | Difference with average = 28-12.4 = 15.6 is very wide, so calculation not required |
(c) Production and Exports of Pulses (In Million kg) has been given below
| Year | 2000-01 | 2001-02 | 2002-03 | 2003-04 | 2004-05 |
| Exports | 114 | 115 | 220 | 180 | 310 |
| Production | 242 | 340 | 640 | 565 | 930 |
Find the average proportion of pulses exported as a fraction of the tea produced in the half decade was (a) 0.11 (b) 0.22 (c) 0.36 (d) 0.41 (e) 0.49
Sol: Here none of the given choices are closer to each other, so mental calculation may work. Just observe that exports are generally 1/3rd of production with one year (1990-91) showing nearly 1/2 of production as exports. Hence the required average will be > 1/3 ( = 0.33). Thus 0.36 looks the closest among the alternatives given.(d) Sectoral Growth Rate of Major Industry Groups (2015-16) are given as
| Sectors | Weights | 2015-2016 |
| Oil | 56.6 | 6.5 |
| Pulses | 24.4 | 7.5 |
| Books | 19 | 8 |
| Overall | 100.00 |
Find the overall weighted industrial growth rate in 2015-16 ?
Sol:Weighted average of X = (w1x1+w2x2+w3x3)/(w1+w2+w3)
Required weighted average growth rate in 2001-02 = (56.6×6.5+24.4×7.5+19×8)/(56.6+24.4+19)
= 702.9/100
= 7.03
Example
Directions(1-5): Study the following table and answer the questions given below in
Production of different types of pulses in a company(figures in thousand)
Year
|
Types of pulses
| ||||
A
|
B
|
C
|
D
|
E
| |
2002
|
180
|
60
|
84
|
100
|
76
|
2003
|
210
|
90
|
32
|
80
|
48
|
2004
|
135
|
30
|
44
|
95
|
85
|
2005
|
190
|
85
|
69
|
125
|
115
|
2006
|
260
|
95
|
120
|
80
|
120
|
2007
|
240
|
140
|
161
|
90
|
185
|
1. In which of the given years was the production of B-type pulses close to its average production over given years?
(a) 2005 (b) 2004 (c) 2003 (d) 2002 (e) None
2. In which year the production of D-type pulses was maximum ?
(a) 2003 (b) 2006 (c) 2005 (d) 2007 (e) 2002
3. What was the approximate percentage of production of A-type pulses in 1995 to its total pulses over the years?
(a) 20 (b) 15 (c) 23 (d) 40 (e) 30
4. In which of the following pairs of years was the total production of E-type pulses two lakhs?
(a) 2003 & 2005 (b) 2005 & 2007 (c) 2004 & 2007 (d) 2002 & 2004 (e) None
5. In which of the given years the total production of all types of scooters was minimum ?
(a) 2004 (b) 2006 (c) 2007 (d) 2005 (e) None
Solution
S-1 (a)average production of B-type pulses over the years (2002-2007) =(60+90+30+85+95+140)/6
= 83 (in thousand)
S-2 (c)
S-3 (b)
Approximate percentage of production of A-type pulses in 2005 to its total production
= Production in 2005 of A-type/Total production of A-type (2002-07)×100
= 190/(180+210+135+190+260+240)×100
= 190/1215×100
= 15
S-4 (e)
| Pairs of years | Total production of E-type pulses |
| 2003 & 2005 | 48 + 115 ≠ |
| 2005 & 2007 | 115 + 185 ≠ |
| 2004 & 2007 | 85 + 185 ≠ |
| 2002 & 2004 | 76 + 84 ≠ |
S-5 (a)
| Year | Total Production of all types pulses |
| 2002 | 180 + 60 + 84 + 100 + 76 = 500 |
| 2003 | 210 + 90 + 32 + 80 + 48 = 460 |
| 2004 | 135 + 30 + 44 + 95 + 85 = 389 → Minimum |
| 2005 | 190 + 85 + 69 + 125 + 115 = 444 |
| 2006 | 260 + 95 + 120 + 80 + 120 = 675 |
| 2007 | 240 + 140 + 161 + 90 + 185 = 816 |
