Line Graphs: Introduction & Examples (with Solutions) - CSAT Preparation - UPSC

What is a Line Graph?

Line Graph is the innovative version of Bar Graph representation. 

If we connect the upper point of the first Bar to the upper point of the second Bar and then tie these dots, we will get a line. Repeating the procedure gives us the Line Graph representation. Line graphs and bar graphs are easy to comprehend. A Line Graph looks like this:

Line Graph

Sample Question

The following line graph shows the ratio of expenditure to income of three companies A, B and C during the period 2008–2013.

Reading the headings is important, otherwise, you will not be able to understand what these lines are all about.

Along Y-Axis are the ratios. Along X-Axis are the years. In between are the lines.

Learn a few things from the heading:

1. For Company A in 2008, if Expenditure is Rs 0.9, then Income will be Rs 1, and so on.
2. It’s Expenditure to Income Ratio expressed as E:I and not Income to Expenditure.
3. To have a Profit, Expenditure is to be less than Income. The reverse is for Loss.
4. Profit and Loss percentages are calculated using the formulas for the same.
   • Profit = Income – Expenditure
   • Profit Percentage = [Profit/Expenditure]*100
   • Loss = Expenditure – Income
   • Loss Percentage = [Loss/Expenditure]*100
5. The lower is the E:I ratio, higher is the profit.

The questions of Expenditure and Income seem difficult to solve. But, let’s apply the above mentioned points to solve the questions in no time!

Examples

Q1. In which of the following years is the percentage loss/profit of Company C the maximum?

[1] 2008
[2] 2009
[3] 2010
[4] 2011
[5] 2012

Solution: 

From point no. 5 above, we conclude that profit is maximum when E:I is minimum which is 0.3 in 2011.
Hence answer is [4].

Q2. If the expenditure of Company A in 2008 and 2009 together is Rs 60 lakhs, then what is its income in 2008 and 2009 together?

[1] Rs 120 lakhs
[2] Rs 150 lakhs
[3] Rs 66.66 lakhs
[4] Data inadequate
[5] None of these

Solution: 

E:I for Company A in 2008 and 2009 is 0.5 and 0.4. This means for Rs 0.5 Expenditure in 2008, Income is Rs 1 in 2008 and for Rs 0.4 Expenditure in 2009, Income is Rs 1 in 2009. But combined Expenditure of 60 lakhs is given. So, ratios being different, it’s not possible to calculate the Income from the combined expenditure. The answer is [4].

Q3. If the expenditure of Company B in 2008 and 2012 together is Rs 60 lakhs then what is its income in 2008 and 2012 together?

[1] Rs 66.66 lakhs
[2] Rs 75 lakhs
[3] Rs 48 lakhs
[4] 96 Rs lakhs
[5] Data inadequate

Solution: 

E:I for 2008 and 2012 is 0.8 and 0.8. Ratios being the same, combined Income from the combined Expenditure can be calculated. Income = E/0.8 = 60/0.8 = 75 lakhs.
The answer is [2].

Q4. In which of the years does Company C gain 100% profit?

[1] 2008
[2] 2009
[3] 2010
[4] 2011
[5] None of these

Solution: 

For 100% profit, E:I ratio must be 0.5 so that I = E/0.5 = 2E. It’s in 2009.
The answer is [2]

Q5. What is the percentage decrease in the percentage profit of Company C from 2009 to 2010?

[1] 75%
[2] 300%
[3] 62.5%
[4] 160%
[5] None of these

Solution: 

E:I of Company C in 2009 = 0.5:1
Profit = 1-0.5 = 0.5
Percentage profit of profit of Company C in 2009 =[0.5/0.5]*100 = 100%
E:I of Company C in 2010 = 0.8:1
Profit = 1-0.8 = 0.2
Percentage profit of profit of Company C in 2009 =[0.2/0.8]*100 = 25%
Percentage decrease = 75%.
The answer is [1].