SSC CHSL Topic Wise Study Material – Quantitative Aptitude – Line Graph

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A line graph is simplistic method of representing the data. It is used to depict continuous changes in the quantity presented in the graph. It is easier to observe trends and patterns using line graph compared to other diagrams.
Often the quantity represent on the graph is measured as a function of time. i.e., The variation in the quantity as time changes. In the line graph, the line going up indicates increase in the quantity, the line going down indicates decrease in the quantity and horizontal line indicates no change in the quantity over that period.

Parts of a Line Graph
Parts of a line graph are classified as
Title The title of the line graph tells us what the graph is about.
Labels The horizontal label across the bottom and the vertical label along the side tell us what kinds of facts are listed.
Scales The horizontal scale across the bottom and the vertical scale along the side tell us how much or how many kinds of facts are there.
Points The points or dots on the graph show us the facts.
Lines The lines connecting the points give estimates of the values between the points
e.g., Various parts of a line graph can be shown with the help of a line graph.

Representation of Data by a Line Graph
The following data shows the number of questions solved by 320 students at the catalyst career in a test on data interpretation.

This information can be represented by the line graph which is shown below.

Representation of Data by a Line Graph

Reference Corner

Directions (Q. NOS. 1 and 2)Study the following graph and answer the questions.SSC (10 + 2) 2013

1.If the imports of company X in 2007 were increased by 40%, what would be the ratio of exports to the increased imports?
(a) 0.25
(b) 0.75
(c) 1.25
(d) 1.75

2. In 2005, the exports of company X were double that of company Y in that year. If the imports of company X during the year were Rs 180 crores, what was the amount (in crore Rs) of imports of company,Y during the year?
(a) 315
(b) 282
(c) 212
(d) 210

Practice Exercise

Directions (Q. Nos. 1 -5) Observe the sales curve carefully and answer the following questions.
Sales History (in units) of Pears, a Brand of Soap in a Particular Year

1. For how many months was the sales value (in units ) at it’s lowest monthly level?
(a) 1
(b) 3
(c) 4
(d) 6

2. The ratio of the number of months in which there was a decrease to the number of months in which there was no decrease in the sales value was
(a) 2:9
(b) 1 : 11
(c) 1 : 5
(d) 3 : 8

3. The total number of soap units sold in the year was
(a) 88000
(b) 92000
(c) 95000
(d) 98000

4. In which month the sale of soap incurred highest percentage increase over the previous month?
(a) March
(b) April
(c) September
(d) November

5. How many months showed no change in the sales volume over the previous months?
(a) Two
(b) Three
(c) Four
(d) Five

Directions (Q. Nos. 6-10) In a school, the periodical examination are held every Second month. In a session during April 2001 -March 2002, a student of class IX appeared for each of the periodical exams. The aggregate marks obtained by him in each periodical exam are represented in the line graph given below.
Marks obtained by student in six periodical exams held in every two months during the year in the session 2010-2011.
Maximum Total Marks in Each Periodical Exam = 500

6. In which periodical exams did the student obtain the highest percentage increase in marks over the previous periodical exams?
(a) June, 10
(b) August, 10
(c) October, 10
(d) December, 10

7. The total marks obtained in February, 11 is what per cent of the total marks obtained in April, 10?
(a) 110%
(b) 112.5%
(c) 115%
(d) 116.5%

8. What is the percentage of marks obtained by the student in the periodical exams of August, 10 and October, 10 taken together?
(a) 73.25%
(b) 75.5%
(c) 77%
(d) 78.75%

9. What are the average marks obtained by the student in all the periodical exams during the session?
(a) 373
(b) 379
(c) 381
(d) 385

10. In which periodical exam, there is a fall in percentage of marks as compared to the previous periodical exam?
(a) None
(b) June, 10
(c) October, 10
(d) February, 11

Directions (Q. Nos. 11 -13) Study the graph carefully answer the questions that follow.
Profit (in Rs lakh) Made by Three Companies Over the Year Profit = Income – Expenditure

11. Profit made by Company A in the year 2007 was what per cent of the total profit made by all the three companies in the year?
(a) 31.25%
(b) 28.24%
(c) 21.43%
(d) None of these

12. If the income of Company A in the year 2010 was Rs 1354300 , what was its expenditure in that year?
(a) Rs 921600
(b) Rs 954300
(c) Rs 648200
(d) None of these

13. What is the per cent increase in profit made by Company B from 2006 to 2010?
(a) 25%
(b) 32%
(c) 23%
(d) None of these

Answers

Hints & Solutions

SSC CHSL Topic Wise Study Material – Quantitative Aptitude – Bar-Diagram

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Bar chart or graph is one of the oldest and most commonly used graph for presenting data. It is a chart with rectangular bars (equidistant from each other) with lengths proportional to the values they represent. The width of the bars is shown merely for attention.
In this method of data representation, the data is plotted on the x and y axis as bars.
One of the axis (normally the x-axis) of the bar diagram represents a discrete variable while the other axis represents the scale for one or more continuous variable. Each bar diagram has title indicating the subject matter represented in the diagram.

Types of Graph/Chart
1. Simple Bar Diagram A simple bar diagram relates to only one variable.
2. Sub-divided Bar Diagram A sub-divided bar diagram is used to represent various parts of total magnitude of a given variable.
3. Multiple Bar Diagram In this type, two or more bars are constructed adjoining each bar either to represent either , different components of a total or to show multiple variables.

Directions (Examples 1 -5) Study the graph and answer the questions given below. ssc (10+2)2011

1. What is the difference in profit between 1983 and 1984 (in lakh of Rs)?
(a) No profit
(b) 5
(c) 10
(d) 15

2. The number of years in which the income is more than the average income of the given years is
(a) one
(b) two
(c) three
(d) four

3. The ratio of the average income of all the years to the average profit is
(a) 24 :13
(b) 48 :17
(c) 12 : 7
(d) 6 : 5

4.Percentage increase in profit in 1986 over 1982 is
(a) 150%
(b) 120%
(c) 100%
(d) 80%

5. The total income exceeds the total expenditure over the years 1982 to 1986 by
(a) Rs 85 lakh
(b) Rs 105 lakh
(c) Rs 115 lakh
(d) Rs 120 lakh

Illustration for Bar Diagram
The diagram above shows the survey of 6 yr for the sales of mobile phones.
Here, x-axis shows the years which were considered for survey and y-axis shows the quantity of sales.

(a) Histogram

To understand histogram, we need to know the word frequency.
Frequency It is the number of occurrences of a repeating event per unit.
Histogram It is a representation of tabulated frequencies. This representation is done with the help of adjacent rectangles erected over discrete intervals.

Different Components of Histogram
Height of the Rectangular Bars It shows frequency density of the interval, i.e., the frequency divided by the
width of the interval.
Area Covered by the Bars This area shows the frequency of the observations in the interval.
Total Area of Histogram This area is equal to the number of data.

Directions (Examples 6-8) In the given histogram, there is survey for the different; family of different income group of a village. Study the graph carefully and answer the questions given below. ssc (1o+2) 2010

6. How many families were surveyed?
(a) 235
(b) 220
(c) 200
(d) 195

7. What is the total number of family whose daily income is Rs 800 or more?
(a) 50
(b) 55
(c) 65
(d) 80

8. What is the percentage of families whose daily income is less than Rs 500?
(a) 90
(b) 45
(c) 30
(d) 20

Important Facts
* If any bar has frequency zero, then no bar will be formed for that class interval.
* In histogram, the minimum and maximum value of interval of bar is called measurement of bars. Frequency density = Frequency of each class (bar)/Number of units of class interval

(b) Frequency Polygon

A frequency polygon shows a frequency distribution emphasizing the overall pattern in the data.
In this polygon fragmented categories are denoted an -Y-axis and frequencies are denoted on y-axis.
A frequency polygon can be constructed by two methods i.e., with the help of a histogram and without help of histogram.

I. Constructions of a Frequency Polygon with the help of Histogram
The frequency polygon is that type of polygon in which a closed two-dimensional figure of straight line segments joining the mid-points of the top of the bars of a histogram. The first point is located on the x-axis and is placed in the middle of the interval which precedes the first bar of the histogram.
The last point is located on the x-axis in the middle of the interval immediately following the last bar of the histogram.

Direction (Example 9) Draw a frequency polygon with the given data.

9.

II. Construction of a Frequency Polygon without help of Histogram
To draw a frequency polygon with the help of given class intervals and frequency, first of all find the centre-point of each class interval, then indicate these point on x-axis with corresponding frequencies on y-axis. Now join the points according to parameters.

Direction (Example 10) Draw a frequency polygon with the given data.

10.

Directions (Examples 11 -14) Given graph shows the yearly premium of an insurance company which is recovered for the insurance of Rs 1000 for different ages. Study the graph and answer the questions given below, ssc (10+2) 2012

11, Premium on Rs 10000 for the people of age 27 is
(a)Rs 460
(b)Rs 45.75
(c)Rs 457.50
(d)Rs 455

12. Two members of a family are of age 25 yr and 30 yr. What will be the premium for both of them for the insurance of Rs 10000 each?
(a) Rs 925
(b) Rs 910.60
(c) Rs 876.25
(d) Rs 885

13.If the person of age 28 yr is replaced by an another person of age 35 yr with an insurance of Rs 1000, then what will be per cent increase in the premium?
(a) 5%
(b) 4.75%
(c) 5.43%
(d) 6.24%

14. What will be the premium for a person of age 31 yr for the insurance of Rs 1000?
(a)Rs 47
(b)Rs 46
(c)Rs 48
(d)Rs 47.75

Important Facts
* The surface under the frequency polygon is exactly the same as the surface of the histogram i.e., it represents the same amount of data.
* Frequency polygon can be drawn with freehand. In frequency polygon, for any class, frequency of the unit class-interval is called frequency density.

Reference Corner

Directions (Q.Nos. 1 -4) Study the table and answer the questions. ssc (10+2)2015

1.The number of years during which the company has its production less than the average production during 1920-1927 is approximately?
(a) 4
(b) 2
(c) 3
(d) 6

2. The average production of steel is
(a) 74.07
(b) 76.09
(c) 77.10
(d) 75.13

3. The difference of the production of steel in the year 1923 and 1924 is x% of 1927. Then, the value of xis approximately
(a) 0.001%
(b) 1%
(c) 0.01%
(d) 0.1%

4. The ratio of production of steel in the year 1924 and 1925 to that of 1923 and 1927 is
(a) 2005 : 2077
(b) 2205 : 2007
(c) 2205 : 2077
(d) 2077 : 2205

Directions (Q. NOS. 5-8) Study the graph and answer the questions. ssc (10+2) 2014

5. What was the pass percentage in year 2008?
(a)75%
(b)78%
(c)33 1/3%
(d)82 6/17%

6. What was the number of third division in year 2006?
(a) 59
(b) 120
(c) 60
(d) 140

7.In which year, did the college have the best result for B.Com.?
(a) 2007
(b) 2006
(c) Both (a) and (b)
(d) 2008

8. How many per cent passed in first division in year 2007?
(a) 16 2/3
(b) 12 1/2
(c) 15 15/19
(d) 11 13/17

Directions (Q. Nos. 9-13) Study the graph carefully and answer the questions given below. SSC (10+2) 2014

9. Number of patients of age between 55 yr to 66 yr, who got admitted to the hospital on that day is
(a) 6
(b) 4
(c) 24
(d) 8

10. Total number of patients of age more than 55 yr, who got admitted to the hospital is
(a) 4
(b) 7
(c) 9
(d) 10

11. Number of patients of age more than 40 yr and less than 55 yr, who got admitted to the hospital on that day is
(a)20
(b)30
(c)15
(d)12

12. Percentage of patients of age less than 45 yr, who got admitted to the hospital on that day is approximately equal to
(a) 14
(b) 20
(c) 37
(d) 62

13. About 11% of the patients who got admitted to the hospital on that particular day were of age
(a) either between 35 yr and 40 yr or between 55 yr and 60 yr
(b) between 60 yr and 65 yr
(c) between 35 yr and 40 yr
(d) between 35 yr and 40 yr and between 55 yr and 60 yr

Practice Exercise

Directions (Q. NOS. 1-5) Study the following graph carefully to answer these questions.

1. Number of students in college B in.the year 2008 is what per cent of total number of students in college B in all the years together? (Round off to two digits after decimal.)
(a) 20.61
(b) 23.79
(c) 21.79
(d) 17.29

2. What is the average number of students in college A for all the years together?
(a) 45000
(b) 50000
(c) 52000
(d) 48000

3. What is the approximate percentage rise in the number of student of college B from 2005 to 2006?
(a) 8
(b) 12
(c) 4
(d) 15

4. For which colleges, and in which year was, the per cent rise in number of students from ‘the previous year the highest? ‘
(a) College A in 2004 and college B in 2005
(b) Only college B in 2004
(c) College A in 2004 anti college B in 2004
(d) College A in 2007 and college B in 2004

5. What is the ratio between the total number of students in college A in the year 2004, 2006 and 2007 together and-the, total number of students in college B in the year 2003, 2004 and 2008, respectively?
(a) 35:32
(b) 33:37
(c) 34:31
(d) 32:35

Directions (Q. Nos. 6-10) Study the following graph and answer the questions that follow.

6.What was the respective ratio between the number of candidates qualified in the written test in the year 2002 for admission in institution B and the number of candidates qualified in the written test in the year 2006 for admission to institution A?
(a) 8:5
(b)7: 4
(c) 7:8
(d) 7 : 5

7. What was the approximate average number of candidates qualified in the written test for admission to institution B over all the year?
(a) 4555
(b) 4200
(c) 4160
(d) 4667

8. In which year, the total number of candidates qualified in the written test for admission to both the institutions together was the second highest?
(a) 2003
(b) 2004
(c) 2005
(d) 2006

9. What is the difference between the total number of candidates qualified in written test in the year 2006 for admission to institutions A and B together and the number of candidates qualified in written test in the year 2003, for admission to institution A?
(a) 5000
(b) 3500
(c) 1500
(d) 5500

10. What was the total number of candidates qualified in the written test for admission to institution A over all the years together?
(a) 27000
(b) 26500
(c) 26000
(d) 27500

Directions (Q. NOS. 11-15) Study the following graph and answer the questions that follow.
Number of Candidates Appeared and Passed[in hundred) in a Test from Seven Different Institutions

11. What is the difference between the number of candidates appeared in institutions B, C, D and F together and candidates passed from institutions A, E and C together?
(a) 100
(b) 900
(c) 1000
(d) 540

12. What is the average number of candidates passed from all the institutions together?
(a) 700
(b) 490
(c) 350
(d) 675

13. Number of candidates passed from institutions C and E together is approximately what per cent of the total number of candidates appeared in institutions A and G together?
(a) 72
(b) 62
(c) 54
(d) 67

14. From which institution, the difference between the appeared candidates and the passed candidates is maximum?
(a) B
(b) C
(c) D
(d) F

15. What is the respective ratio of the number of candidates who got failed from institution B to the number of candidates who have appeared in institution F?
(a) 2 : 5
(b) 2 : 3
(c) 4 : 3
(d) 1 : 3

Directions (Q. Nos. 16-19) The following chart represents the number of students of AMS Careers at its Lucknow center who passed the CAT exam or the XAT exam or the CET exam or none of these exams. (Assume that there are no students who passed more than one exam.)

16. What was the percentage of students who cleared CAT in 2010?
(a) 19.50%
(b) 12.65%
(c) 14.28%
(d) 11.76%

17. What was the percentage of students who succeeded in at least one of the three exams in 2010?
(a) 82.4%
(b) 82,8%
(c) 82.35%
(d) 83.3%

18. Which year showed the best result in MBA entrance exams for the institute (in terms of percentage of students who cleared)?
(a) 2010
(b) 2011
(c) 2012
(d) Cannot be determined

19. What is the percentage increase in the number of students in 2012 over 2010?
(a) 30%
(b) 17.64%
(c) 117.6%
(d) 85%

Directions (Q. NOS. 20-22) The following chart figure shows the production of cars in thousands.

20. The ratio of Hindustan Motor’s production in 2011-12 to Honda’s production in 2010-11 is
(a) 0.66
(b) 1.5
(c) 2
(d) None of the above

21. For how many companies has there been no decrease in production in any year from the previous year?
(a) One
(b) Two
(c) Three
(d) Four

22. How many companies have shown production ,below their average production in 2010-11, but have showed a boy average production in 2011-12?
(a) One
(b) Two
(c) Three
(d) Four

Directions (Q. NOS. 23-27) The following is a horizontal bar diagram showing the accidents in which two wheelers are involved with other objects. Study the diagram and answer the questions. ssc (10+2) 2012

23. The percentage of accidents in which pedestrians and cyclists are involved is
(a) 60%
(b) 20.4%
(c) 24%
(d) 6%

24.The percentage by which the accidents involving buses is less than the accidents involving tanker lorry is
(a) 40%
(b) 28%
(c) 6%
(d) 4%

25.The difference in percentage between the accidents involving two wheelers and other objects is respectively.
(a) 54% more
(b) 54% less
(c) 77% more
(d) 77% less

26. 60% of the accidents happened due to
(a) two wheelers, cars, buses and stationary vehicles
(b) two wheelers, cars, buses and tanker lorry
(c) cars, buses, tanker lorry and pedestrians
(d) cars, tanker lorry, bicycles and stationary vehicles

27. If the data of the bar diagram is represented by a pie chart and the angle of a sector of the pie chart is 36°, then this sector represents the accidents involving
(a) buses
(b) stationary vehicles
(c) pedestrians
(d) bicycles

Directions (Q. Nos. 28-32) In the histogram below marks obtained by 45 students of a class is given. Study the histogram and answer the questions given below.

28.How many students got less than 10 marks?
(a) 2
(b) 10
(c) 1
(d) 4

29.How many students got more than 30, but less than 40 marks?
(a) 3
(b) 4
(c) 5
(d) 6

30.How many students got 50 or more marks?
(a) 9
(b) 10
(c)11
(d) 16

31.If the minimum passing marks are 30, then how many students failed in the examination?
(a) 2
(b) 6
(c) 18
(d) 20

32.If the minimum passing marks are 30, then what is the percentage of passed students?
(a) 75%
(b) 60%
(c) 50%
(d) 40%

Answers

Hints & Solutions

SSC CHSL Topic Wise Study Material – Quantitative Aptitude – Problem Based on Ages

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In ‘problems based on ages’ usually relationships between the ages or two or more persons at two different time are given and we are required to find the ages of these persons. Such problems can be Solved by the knowledge of ‘Linear Equations’. In these problems there may be three situations
1. Age some years ago
2. Present age
3. Age some years hence
Two of these situations are given and it is required to find the third. The relation between the age of two persons may also be given. Simple linear equations are framed and their solutions are obtained. Sometimes, short-cut methods given below are also helpful in solving such problems.

Some Useful Facts/Formulae

• The age of A, t yr ago, was n₁ times the age of B and at present A’s age is n₂ times that of B, then
  A’s present age = (n₁-1/n₁-n₂)n₂ t yr and B’s present age = (n₁-1/n₁-n₂) t yr

Example The age of father is 4 times the age of his son. If 5 yr ago father’s age was 7 times the age of his son at that time, what is father’s present age?
(a) 36 yr
(b) 40yr
(c) 42yr
(d) 48yr

• The present age of A is n₁ times the present age of B. If t yr hence, the age of A would be n₂ times that of B, then
  A’s present age=(n₂-1/n₁-n₂)n₂ t yr and B’s present age=(n₂-1/n₁-n₂) t yr

Example The age of Mr. Gupta is four times the age of his son. After 10 yr, the age of Mr. Gupta will be only twice the age of his son. Find the present age of Mr. Gupta’s son.
(a) 6 yr
(b) 5 yr
(c) 4 yr
(d) 8 yr

• The age of A, t₁ yr ago, was n₁ times the age of B. If t₂ yr, hence A’s age would be n₂ times that of B, then
  

Example 10 yr ago, Anu’s mother was 4 times older than her daughter. After 10 yr, the mother will be twice older than the daughter. Find the present age of Anu.
(a) 20 yr
(b) 22 yr
(c) 24 yr
(d) 28 yr

• The sum of present age of A and B is S yr. If, t yr ago, the age of A was n times the age of B, then
  Present age of A = S_n-t(n-1)/n+1 yr and present age of
  B =S + t(n- 1)/n+1 yr

Example The sum of the ages of A and B is 42 yr. 3 yr back, the age of A was 5 times the age of B. Find the difference between the present age of A and B.
(a) 22 yr
(b) 28yr
(c) 25yr
(d) 24yr

Reference Corner

1. The average age of P, Q and R is 5 yr more than R’s age. If the total ages of P and Q together is 39 yr, then R’s age is SSC (10 + 2) 2014
(a) 16 yr
(b) 14 yr
(c) 12 yr
(d) 24 yr

2.The average age of A and B is 20 yr. If A is to be replaced by C, the average would be 19 yr. The average age of C and A is 21 yr. The ages of A, B and C in order (in yr) are SSC (10 + 2) 2013
(a) 22,18, 20
(b) 22, 20,18
(c) 18, 22, 20
(d) 18, 20, 22

Practice Exercise

1. Sachin was twice as old as Ajay 10 yr back. How old is Ajay today if Sachin will be 40 yr old 10 yr hence?
(a) 20 yr
(b) 10 yr
(c) 30 yr
(d)None of these

2. Sister’s age is 3 times that of her brother’s. After 5 yr the sister shall be twice as old as her brother. How many years before, the sister’s age was 6 times of her brother’s age? .
(a) 1
(b) 3
(c) 5
(d) 10

3. The average age of the mother and her 6 children is 12 yr which is reduced by 5 yr, if the age of the mother is excluded. How old is the mother?
(a) 42 yr
(b) 40 yr
(c) 48 yr
(d) 50 yr

4. A father’s age is three times the sum of the ages of his two children, but 20 yr, hence his age will be equal to the sum of their ages. Then, the father’s age is
(a) 30 yr
(b) 40 yr
(c) 35 yr
(d) 45 yr

5. The age of A, B and C together total 185 yr. B is twice as old as A and C is 17 yr older than A Then, The respective ages of A, B and C are
(a) 40 yr, 86 yr and 59 yr
(b) 42 yr, 84 yr and 59 yr
(c) 40 yr, 80 yr and 65 yr
(d) None of the above

6. 1 yr ago a father was four times as old as his son. In 6 yr times his age exceeds twice his son’s age by 9 yr. Ratio of their ages is
(a) 13 : 4
(b) 12 : 5
(c) 11 : 3
(d) 9 : 2

7. The sum of ages of a father and son is 45 yr. 5 yr ago, the product of their ages was four times the father’s age at that time. The present age of the father is
(a) 39 yr
(b) 36 yr
(c) 25 yr
(d) None of these

8. 5 yr ago Mr. Sohanlal was thrice as old as his son and 10 yr, hence he will be twice as old as his son. Mr. Sohanlal’s present age (in yr) is
(a) 35
(b) 45
(c) 50
(d) 55

9. If 6 yr are subtracted from the present age of Randheer and the remainder is divided by 18, then the present age of his grandson Anup is obtained. If Anup is 2 yr younger to Mahesh whose age is 5 yr, what is the age of Randheer?
(a) 84 yr
(b) 48 yr
(c) 60 yr
(d) 96 yr

10. If 1 is added to the age of the elder sister, then the ratio of the ages of two sisters becomes 0.5 : 1, but if 2 is subtracted from the age of the younger one, the ratio becomes 1 : 3. Find the age of the two sisters.
(a) 8 yr and 5 yr
(b) 11 yr and 6 yr
(c) 9 yr and 5 yr
(d) 8 yr and 6 yr

11. The ratio of the ages of the father and the son at present is 7:1. After 4 yr, the ratio will become 4:1. What is the sum of the present ages of the father and the son?
(a) 29 yr
(b) 35 yr
(c) 32 yr
(d) None of these

12. Anil is at present one-fourth the age of his father. After 16 yr, he will be one-half age of his father. Find the present age of Anil’s father.
(a) 40 yr
(b) 36 yr
(c) 32 yr
(d) 28 yr

13. Honey was twice as old as Vani 10 yr ago. How old is Vani today, if Honey will be 40 yr old 10 yr hence?
(a) 25 yr
(b) 20 yr
(c) 15 yr
(d) 35 yr

14. The age of the father 5 yr ago was 5 times the age of his son. At present the father’s age is 3 times that of his son. What is the present age of the father?
(a) 33 yr
(b) 30 yr
(c) 45 yr
(d) None of these

15. The age of a man is 3 times that of his son. 15 yr ago, the man was 9 times as old as his son. What will be the age of the man sifter 15 yr?
(a) 45 yr
(b) 60 yr
(c) 75 yr
(d) 65 yr

Answers

Hints & Solutions

SSC CHSL Topic Wise Study Material – Quantitative Aptitude – Table

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Tables are one of the simplest and most convenient tools used for summarizing data and presenting it in a meaningful way. In a table, data is arranged systematically in columns and rows. While reading a table, the following parts need careful observation
Title The title of the table gives the description of the contents of the table and precisely defines the kind of data and the period for which it occurred.
Column Heading It defines the information contained in the various columns and specifies the unit of measurement in some cases.
Head Note Most frequently, the unit of measurement is specified in the head note.
Foot Note Foot notes are used to point out any exceptions in arriving at the data.

Illustration for Table
Percentage of Marks Obtained by Five Students in Five Different Subjects

Thus, from the table above we can derive, any information regarding marks of the mentioned students.

Reference Corner

Directions (Q. Nos. 1 and 2) The table shows the percentage of total population of a city in different age groups. Study the table and answer questions. ssc (10+2) 2013

1. If there are 22 million people below 36 yr, then the number of people (in millions) in the age group 56 – 65 is
(a) 3
(b) 3.5
(c) 5
(d) 5.5

2. If the difference between the number of people in the age groups 46-55 and 16-25 is 0.975 million, then the total population (in millions) of the city is
(a) 22
(b) 25
(c) 27
(d) 30

Directions (Q. Nos. 3 and 4) Study the following table. SSC (10 + 2) 2013

3. The increase in the number of candidates qualified under Engineering discipline from 2009 to 2010 was
(a) 28
(b) 30
(c) 46
(d) 49

4. The number of candidates qualified in Science discipline was the lowest in the year
(a) 2006
(b) 2008
(c) 2009
(d) 2010

Practice Exercise

Directions (Q. Nos. 1-5) The table given here shows production of five types of cars by a company in the year . 1999 to 2004 Study the table and answer the questions.
Production of Cars by a Company

1. In which year, the production of cars of all types taken together was approximately equal to the average during the period?
(a) 1999
(b) 2001
(c) 2003
(d) 2004

2. In which year the total production of cars of types P and Q together was equal to the total production of cars of types R and S together?
(a) 2000
(b) 2001
(c) 2004
(d) None Of these

3. During the period 1999-2004 in which type of cars was a continuous increase in production?
(a) P
(b) Q
(c) R
(d) S

4. The production of which type of cars was 25% of the total production of all types of cars during 2003?
(a) S
(b) R
(c) Q
(d) P

5. The per cent increased in total production of all types of cars in 2002 to that in 2001 was
(a) 15
(b) 20
(c) 25
(d) 30

Directions (Q. Nos. 6-9) Answer the questions based on the following information. Given below are the forecasts of the World and Asian energy demand for the years 1990,2000 and 2010 AD. The demand is given in million barrels per day, crude oil equivalent.

6. Which is the fuel whose proportion in the total energy demand will decrease continuously over the period 1990-2010 in Asia?
(a) Natural Gas
(b) Solid Fuels
(c) Nuclear
(d) Hydropower

7. Which is the fuel whose proportion in the total energy demand of the World will remain constant over the period 1990-2010, but whose proportion will increase in total energy demand in Asia?
(a) Solid Fuels
(b) Nuclear
(c) Hydropower
(d) Natural Gas

8. Over 1990-2010, which two fuels meet more than 60% of the total energy demand of both World and Asia?
(a) Petroleum and Natural Gas
(b) Petroleum and Solid Fuels
(c) Natural Gas and Solid Fuels
(d) None of the above

9.Which fuel’s proportion in the total energy demand increase over the decade 1990-2000 and decrease over the decade 2000-2010 for both World and Asia?
(a) Petroleum
(b) Natural Gas
(c) Solid Fuels
(d) Nuclear

Directions (Q. Nos. 10-13) Answer the questions based on the following information.
A company produces five types of shirts A, B, C, D, and E, using the cloth of three qualities—high, medium and low and dyes of the three qualities—high, medium and low One shirt requires 1.5 m cloth. The following table gives respectively
I. The number of shirts (of each category) produced in thousand
II. The percentage distribution of cloth quality in each type of shirt.
III. The percentage distribution of dye quality in each type of shirt.

10. What is the total requirement of cloth?
(a) 150000 m
(b) 200000 m
(c) 225000 m
(d) 250000 m

11. How many metres of low-quality cloth is consumed?
(a) 22500
(b) 46500
(c) 60000
(d) 40000

12. How many metres of high-quality cloth is consumed by A shirts?
(a) 8000
(b) 112000
(c) 24000
(d) 30000

13. What is the ratio of the three qualities of dyes in high-quality cloth?
(a) 2 : 3 : 5
(b) 1 : 2 : 5
(c) 7 : 9 : 10
(d) Cannot be determined

Directions (Q. Nos. 14-18) Answer the questions based on the following table.
Distribution of Students at ABC University According to Professional Courses

14. If 60% of the boys mid 70% of the girls are successful in the courses taken by them, then what is the combined pass percentage (approximately)?
(a) 67.2
(b) 63.1
(c) 62
(d) 68.5

15. In which course is the percentage of girls (among the total number of students) higher than the percentage of girls in any other course?
(a) business Management
(b) computers
(c) science
(d) others

16. By what percentage is the number of students doing Computers more them the number of students doing Business Management?
(a) 67.2
(b) 63.1
(c) 62
(d) 68.5

17. The percentage of girl engineers doing Business Management are
(a) 11.2
(b) 12.2
(c) 15
(d) None of these

18. Taking all the courses together, by what percentage do the number of boys exceed the number of girls?
(a) 521.4%
(b) 421.4%
(c) 321.4%
(d) None of these

Directions (Q. Nos. 19 22) Study the following table and answer the questions given below. ssc (1o+2) 2011
Marks Obtained by 6 Candidates (A, B, C, D, E and F) in 6 Tests Conducted in One Academic Year.

19. The total marks obtained by the candidates B and F together was the least in the Test
(a) 2
(b) 3
(c) 4
(d) 5

20. Which of the candidates has shown a steady improvement throughout the academic year?
(a) A
(b) B
(c) C
(d) D

21. Which candidate has shown maximum percentage improvement in Test 6 compared to Test 1?
(a) A
(b) E
(c) B
(d) C

22. In which Test have all candidates performed better than in the previous Test?
(a) Test 6
(b) Test 5
(c) Test 4
(d) Test 2

Answers

Hints & Solutions

SSC CHSL Topic Wise Study Material – Quantitative Aptitude – Height and Distance

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Height and distance is an essential component of Trigonometry.
In this chapter trigonometric properties are used for finding height and distances of various objects without actually measuring it. Sometimes we are required to find the height of a tower, tree, building and distance of a ship from light house, width of a river.

Concept of Pythagoras Theorem
In a right angled triangle, the square of its hypotenuse is equal to the sum of the squares of its legs (i.e., perpendicular and base).

In other words, (Hypotenuse)² = (Perpendicular)² + (Base)²
=> (BC)² = (AB)² + (AC)² => h²=p² + b²
Pythagoras theorem is used for solving most of the problems of height and distance.

Angle of Elevation The angle of elevation of the point viewed is the angle formed by the line of horizontal, when the point being is above the horizontal level.

Example A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30°. The man walks some distance towards the tower and then his angle of elevation of the top of the tower is 60°. If the height of the tower is 30 m, then the distance he moves is
(a) 20 m
(b) 20√3 m
(c) 22 m
(d) 22√3 m

Angle of Depression When the line of sight is below the horizontal level, the angle so formed by the line of sight with the horizontal is called the angle of depression.

Example From a point A on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45°, respectively. If the bridge is at a height of 9 m from the banks, find the width of the river.
(a) 24.588 m
(b) 23.458 m
(c) 25.458 m
(d) 28.885 m

Reference Corner

1. TF is a tower with F on the ground. The angle of elevation of T from A is x° such that tan x° = 2/5 and AF= 200 m. The angle of elevation of T from a nearer point B is y° with BF = 80 m. The value of y° is SSC (10 + 2) 2015
(a) 75°
(b) 45°
(c) 60°
(d) 30°

2.A tree of height h m is broken by a storm in such a way that its top touches the ground at a distance of x m from its root. Find the height at which the tree is broken. (Here, h > x) SSC (10+2) 2014
(a)h²+x²/4h m
(b)h²-x²/4h m
(c)h²+x²/2h m
(d)h²-x²/2h m

3. The angle of elevation of the top of a tower from a point on the ground is 30° and moving 70 m towards the tower it becomes 60°. The height of the tower is SSC (10+2) 2014
(a) 10√3 m
(b) 35√3 m
(c) 10 m
(d) 10/√3 m

4. From two points on the ground and lying on a straight line through the foot of a pillar, the two angles of elevation of the top of the pillar are complementary to each other. If the distances of the two points from the foot of the pillar are 9 m and 16 m and the two points lie on the same side of the pillar, then the height of the pillar is SSC (10 + 2) 2013
(a) 7 m
(b) 12 m
(c) 5 m
(d) 10 m

Practice Exercise

1. The angle of elevation of the top of a tower at a point D on the ground is 30°. On walking 20 m towards the tower the angle of elevation becomes 60°. The height of the tower is equal to
(a)10/√3 m
(b)20√3 m
(c)20/√3 m
(d)10√3 m

2. A radio transmitter antenna pf height 100 m stands at the top of a tall building. At a point on the ground, the angle of elevation of bottom of the antenna is 45° and that of top of antenna is 60°. What is the height of the building?
(a) 100 m
(b) 50 m
(c) 50 (√3 + 1) m
(d)50 (√3 – 1)m

3. The angle of elevation of a jet fighter from a point P on the ground is 60°. After 5 s of flight, the angle of elevation changes to 45°. If the jet is flying at a height of 3000 m, then the speed of the jet (in m/s) is
(a) 1000 (3 – √3)
(b) 200 (3 – √3)
(c)1000√3
(d) 600

4. From the mast head of ship, the angle of depression of a boat is 60°. If the mast head is 150 m, then the distance of the boat from the ship is
(a) 86.6 m
(b) 68.6 m
(c) 66.8 m
(d) None of these

5. A telegraph post gets broken at a point against a storm and its top touches the ground at a distance 20 m from the base of the post making an angle 30° with the ground. What is the height of the post?
(a) 40/√3 m
(b) 20√3 m
(c) 40√3 m
(d) 30 m

6. A portion of a 30 m long tree is broken by tornado and the top struck up the ground making an angle 30° with ground level. The height of the point where the tree is broken, is equal to
(a)30/√3m
(b)10m
(c) 30√3 m
(d) 60 m

7. The angle of elevation of the top of a tower from the bottom of a building is twice that from its top. What is the height of the building if the height of the tower is 75 m and the angle of elevation of the top of the tower from the bottom of the buildings is 60°?
(a) 25 m
(b) 37.5 m
(c) 50 m
(d) 60 m

8. The shadow of a tower is 15 m when the elevation is 30°. What is the length of the & when the sun’s elevation is 60°?
(a) 3 m
(b) 4 m
(c) 5 m
(d) 6 m

9. Two posts are 25 m and 15 m high and the joining their tips makes an angle of 45° horizontal. The distance between these posts is
(a) 5 m
(b) 10/√2 m
(c) 10 m
(d)10√2 m

10. The poles of heights 6 m and 11 m stand vertically upright on a plane ground. If the distance between their feet is 12 m. What is the distance between their tops?
(a) 11 m
(b) 12 m
(c) 13 m
(d) 14 m

11. The height of a tower is h and the angle of elevation of the top of the tower is α. On moving a distance h/2 towards the tower, the angle of elevation becomes β. What is the value of (cot α – cot β)?
(a)1/2
(b)2/3
(c)1
(d)2

12. A vertical post 15 ft high is broken at a certain height and its upper part, not completely separated, meets the ground at an angle of 30°. Find the height at which the post is broken. SSC (10 + 2) 2012
(a) 10 ft
(b) 5 ft
(c) 15√3 (2 – √3) ft
(d)5√3 ft

13.The angles of elevation of the top of a building from the top and bottom of a tree are x and y, respectively. If the height of the tree is h m, then in metre, the height of the building is SSC (10+2) 2011

Answers

Hints & Solutions