Solving Data Interpretation problems is a relatively more time consuming yet a highly scoring part of Quantitative Ability section. In the exam, you can expect at least 2 full fledged sets having 4-5 questions each.
Few tips to approach such problems:
- Approximation: You can rely on visual approximation when bar graphs and line charts are in question. For this, before you start calculating, you must try and eliminate a few options based on visual clues.Some options provided in the question can be easily ruled out by just looking at the pie chart or line graph. Usually you are left with just close options out of which one will be the solution. So just do detailed calculation for these 2 options to save time.
- Interpretation: You should first read and interpret the data and do not blindly start solving. Don’t miss out on any statement given in the question. Basically, once you simplify the given data, you have solved the problem. Questions then remain mere formality.
- Learn tables till 20. Learn fractions till 1/20 to improve your speed. And waste little time in finding averages. For eg. finding averages like:
What you usually do: [80+75+95+85+75+70]/6
Rather: 70 + [10+5+25+15+5]/6=70+ [60/6]= 80
- It is usually seen that the answer to the first question is useful in solving the next question. So it is advisable that you solve the questions in the order in which they appear.
Let’s learn about percentages and fractions a bit.
WHAT IS PERCENTAGE? |
- Percentage=Percent=Per Hundred e.g. if we say that Amit has scored 80% marks. We mean to say he has scored 80 marks over 100 marks.
- In every Cricket match, we see strike rates of Batsman, Strike rate is actually a percentage. (Although it is not called that strike rate of Player X is 88 %). If strike rate of a player is 88, it means he on average makes 88 runs over 100 balls.
In the above figure. Each quarter represents 25% of the area of the circle.
In other way we can also say that each quarter of circle has ¼ of the total area of the Circle.
So, Area of a Quarter of Circle= ¼ of Total Area of Circle= 25% of the total area of the Circle.
So, either we calculate 25% of something or 1/4^{th} of it both are one and same.
I.e. Fraction equivalent of 25% is equal to 1/4.
HOW TO CONVERT A FRACTION INTO PERCENTAGE? |
To convert any fraction into equivalent percentage multiply that fraction by 100.
Example:
Fraction | Calculation | Percentage |
1/5 | 1/5 X 100 | 20 % |
1/8 | 1/8 X 100 | 12.5 % |
3/4 | 3/4 X 100 | 75 % |
HOW TO CONVERT PERCENTAGE INTO FRACTION? |
To convert any percentage into equivalent fraction, divide that percentage by 100.
Example:
Percentage | Calculation | Fraction |
20 % | 20/100 | 1/5 |
25 % | 25/100 | 1/4 |
40 % | 40/100 | 2/5 |
12.5 % | 12.5/100 | 1/8 |
ADVANTAGE OF ABOVE CONVERSIONS? |
- Many of you would be thinking , what is the benefit of learning
Fraction ====> Percentage ====> Fraction conversions, when we already know the traditional method to calculate percentages. To show the advantage of the above conversions. Let us take an example.
Example 1: If population of Vatican City is 960.If population of Vatican City grows by 12.5 % in a year. Calculate the population after one year.
Solution:
Traditional Method:
Population after one year = 960 + 12.5% of 960
= 960 + 12.5/100 X 960
= 960 + 120 = 1080 Ans.
In traditional method we need to do tedious calculation, but our conversion makes it so easy.
Using Conversion Method: In above section we have seen that 12.5 % is equivalent to 1/8 in fraction. I have earlier discussed that calculating 12.5 % of any number is exactly same as calculating 1/8 of that number.
Population after one year = 960 + 1/8 X 960 = 960 + 120 = 1080 Ans.
Actually you need not to write anything on the paper, let’s see how you should calculate mentally.
12.5% increase = 1/8 increase
1/8 of 960 = 120
Total Population after a year = 960 + 120 = 1080
Conversion Table
Fraction | Percentage | Fraction | Percentage | Fraction | Percentage | Fraction | Percentage |
1/2 | 50 % | 1/11 | 9.09 % | 1/20 | 5.00 % | 5/8 | 62.5 % |
1/3 | 33.33 % | 1/12 | 8.33% | 1/21 | 4.76 % | 7/8 | 87.5 % |
1/4 | 25 % | 1/13 | 7.69 % | 1/22 | 4.54 % | 2/3 | 66.66 % |
1/5 | 20 % | 1/14 | 7.14 % | 1/23 | 4.35 % | 5/6 | 83.33 % |
1/6 | 16.67 % | 1/15 | 6.66 % | 1/24 | 4.166 % | 4/5 | 80 % |
1/7 | 14.28 % | 1/16 | 6.25 % | 1/25 | 4.00 % | ||
1/8 | 12.5 % | 1/17 | 5.88 % | 1/30 | 3.33 % | ||
1/9 | 11.11 % | 1/18 | 5.55 % | 3/8 | 37.5 % | ||
1/10 | 10 % | 1/19 | 5.26 % | 2/5 | 40 % |
Let us take one question:
Question: Above Graph represents No. of units sold by Bajaj Auto in different segment from 2005 to 2008.
Ques1: In 2005, Scooters sales in volume is how much percentage of total sales.
a)65 % b) 46.82% c) 56.37% d) 59.82%
Solution: In 2005, Scooters= 482
Total Sales= Scooters + Mopeds + Three Wheelers
= 482 + 245 + 128
=855
So, Answer = 482/855 x 100
Ultimately, you are required to perform division to get the answer.
Now, I will discuss how to calculate the value of 482/855.
Step 1: Approximate your denominator to nearest century number. In this case approximate 855 to 900.
Step 2: Calculate approximate value of the given fraction, in this case take numerator 500 and denominator 900. So approximate value of the given fraction will be 5/9.
Step 3: If a fraction x/y is given and you increase/decrease the numerator and denominator in the ratio x : y the value of fraction does not change.
Let us understand it taking an example:
Given ratio: 5/9
If I increase numerator by 5 and denominator by 9 , new fraction = 10/18= 5/9
If I increase numerator by 10 and denominator by 18 , new fraction = 15/27= 5/9
If I increase numerator by 25 and denominator by 45 , new fraction = 30/54= 5/9
If I decrease numerator by 15 and denominator by 27 , new fraction = -10/-18= 5/9
Step 4: Since we have calculated approximate value of fraction= 5/9.
Above calculation division becomes easy if you make denominator 900.
482/855= (482+x)/900
Increase in denominator = 900 – 855 = 45
So, if increase in numerator = 25 ;the value of fraction will not change. (since25/45=5/9 as discussed in step 3)
482/855 = (482+25)/(855+45) = 507/900 = 0.5633
So, Answer will be 56.33%
If you use calculator and find the exact value of fraction 482/855= 0.5637.
So, what we calculated using approximation is very close to actual value. If you look at the options,
You got the answer which is option [C]
So if you practice above method you can calculate any fraction very easily.
Question2: What is percentage increase in sales of scooter in 2008 w.r.t. 2007?
a)25% b) 28% c) 31% d) 29%
Solution: % increase in sales = (614-476)/476 * 100
= 138/476 * 100
Approximate value of 138/476 = 150/500 = 3/10 = 0.3/1
138/476 = (138+x)/500
Increase in denominator = 500 – 476 = 24
Corresponding Increase in Numerator= 24 x 0.3 = 7.2
So, 138/476 = (138+7.2) / (476+24) = 145.2/500 = 0.2904
Answer = 29.04 %
Hence option D is correct.
Let’s learn about how to deal with successive percentage increase/ Decrease.
Let us understand first concept of Multiplying Factor (M.F.)
Case 1: When a quantity is increased by certain percentage.
A) Suppose we have to increase a value 120 by 10%. What will be the final value?
Final Value= Initial Value + 10% of Initial Value
= 120 + 10% of 120
=120 (1+ 10%)
=120(1+10/100)
=120(1.1)
=120 x 1.1=132
So now we can say for 10% increase if we multiply initial value by 1.1 we will get our final value.
So, here we call 1.1 as Multiplying Factor (M.F.)
Note: For 10% increase Multiplying Factor =1.1
B) Suppose we have to increase a value 120 by 20%. What will be the final value?
Final Value= Initial Value + 20% of Initial Value
= 120 + 20% of 120
=120 (1+ 20%)
=120(1+20/100)
=120(1+0.2)
=120 x 1.2=144
So now we can say for 20% increase if we multiply initial value by 1.2 we will get our final value.
So, here we call 1.2 as Multiplying Factor (M.F.)
Note: For 20% increase Multiplying Factor =1.2
Let us generalize the above case.
So, if we increase our initial value by x%. What will be our final value?
Final Value= Initial Value + x% of Initial Value
= Initial Value (1+ x %)
= Initial Value (1+ x/100)
So, if we increase a value by x%.
To get Final Value we need to Multiply Initial value by Multiplying Factor .
Multiplying Factor= 1+x/100.
Case 2: When a quantity is decreased by certain percentage.
A) Suppose we decrease 120 by 10%. What will be the final value?
Final Value= Initial Value – 10% of Initial Value
= 120 – 10% of 120
=120 (1 – 10%)
=120(1-10/100)
=120(1- 0.1)
=120 x 0.9=108
So now we can say for 10% decrease if we multiply initial value by 0.9, we will get our final value.
So, here we call 0.9 as Multiplying Factor (M.F.)
Note: For 10% decrease Multiplying Factor = 0.9
B) Suppose we have to decrease a value 120 by 20%. What will be the final value?
Final Value= Initial Value – 20% of Initial Value
= 120 – 20% of 120
=120 (1 – 20%)
=120(1-20/100)
=120(1-0.2)
=120 x 0.8=96
So now we can say for 20% decrease if we multiply initial value by 0.8 we will get our final value.
So, here we call 0.8 as Multiplying Factor (M.F.)
Note: For 20% decrease Multiplying Factor =0.8
Let us generalize the above case.
So, if we decrease our initial value by x%. What will be our final value?
Final Value= Initial Value – x% of Initial Value
= Initial Value (1- x %)
= Initial Value (1 – x/100)
So, if we decrease a value by x%.
To get Final Value we need to Multiply Initial value by Multiplying Factor .
Multiplying Factor= 1-x/100.
Summary:
Case 1: for x% increase Multiplying Factor= 1+ x/100
Case 2: for x% decrease Multiplying Factor= 1- x/100
Let us make a table for Case 1 & 2
If initial Value is increased by x%:
X% increase | M.F. for X% INCREASE= 1+x/100 | Final Value= Initial Value x Multiplying Factor |
5% | 1+5/100 = 1.05 | Initial Value x 1.05 |
9% | 1+9/100 = 1.09 | Initial Value x 1.09 |
10% | 1+10/100 = 1.1 | Initial Value x 1.1 |
15% | 1+15/100 = 1.15 | Initial Value x 1.15 |
20% | 1+20/100 = 1.20 | Initial Value x 1.20 |
25% | 1+25/100 = 1.25 | Initial Value x 1.25 |
30% | 1+30/100 = 1.30 | Initial Value x 1.30 |
50% | 1+50/100 = 1.50 | Initial Value x 1.50 |
75% | 1+75/100 = 1.75 | Initial Value x 1.75 |
95% | 1+95/100 = 1.95 | Initial Value x 1.95 |
100% | 1+100/100 = 2 | Initial Value x 2 |
150% | 1+ 150/100 = 2.5 | Initial Value x 2.5 |
200% | 1+200/100 = 3 | Initial Value x 3 |
If initial Value is decreased by x%:
X% decrease | M.F. for X% decrease= 1-x/100 | Final Value= Initial Value x Multiplying Factor |
5% | 1 – 5/100 = 0.95 | Initial Value x 0.95 |
9% | 1 – 9/100 = 0.91 | Initial Value x 0.91 |
10% | 1 – 10/100 = 0.9 | Initial Value x 0.9 |
15% | 1 – 15/100 = 0.85 | Initial Value x 0.85 |
20% | 1 – 20/100 = 0.80 | Initial Value x 0.80 |
25% | 1 – 25/100 = 0.75 | Initial Value x 0.75 |
30% | 1 – 30/100 = 0.70 | Initial Value x 0.70 |
50% | 1 – 50/100 = 0.50 | Initial Value x 0.50 |
75% | 1 – 75/100 = 0.25 | Initial Value x 0.25 |
95% | 1 – 95/100 = 0.05 | Initial Value x 0.05 |
100% | 1 – 100/100 = 0 | Initial Value x 0 |
150% | 1 – 150/100 = -0.5 | Initial Value x -0.5 |
200% | 1 – 200/100 = -1 | Initial Value x -1 |
Let’s take an example
Example: XYZ motors limited sold 7000 Scooters in year 2012. If sale of scooter is increases by 10% in year 2013. Calculate no of scooters sold in 2013.
Solution: Increase in scooter sale = 10% ===è M.F. = 1.1
Final Value = Initial Value * M.F.
Scooter sales in 2013 = M.F. X 7000 = 1.1 X 7000 = 7700.
Let us understand how to use Multiplying Factor while solving DI questions.
Example: The below Graph represents Bajaj Auto’s sales volume in different segment from year 2010 to 2013.
Question: What is percentage growth in sales volume of scooter in year 2011 w.r.t. 2010
a) 9% b) 10% c) 15% d) 20%
Solution:
Normal Procedure: No. of Scooter Sold in 2010 = 7000
No. of Scooter Sold in 2011 = 7700
% Increase = [(No. of units sold in 2011 – No. of units sold in 2010) / No. of units sold in 2010] * 100
= [( 7700 – 7000 ) / 7000] * 100 = [700/7000] * 100 = 10 %.
Using Multiplying Factor Method:
Final Value = Initial Value * M.F.
M.F. = Final Value / Initial Value
Note: If final Value and initial Values are given you can calculate Multiplying Factor by dividing Final Value and Initial Value. Once you Got Multiplying Factor you can easily tell % increase or % Decrease.
Let us solve above problem using multiplying factor.
M.F. = Final Value/ Initial Value = 7700 / 7000 = 1.1
If Multiplying Factor = 1.1 ==è 10% increase. ( 1.1-1=0.1*100 = 10 )
(You can do it mentally no need to raise your pen).
Initially it may appear to you that your normal method is also very fast while solving above questions. So, for showing the effectiveness of Multiplying Factor method let us solve another question.
Question: What is percentage change in sales volume of motorcycle in year 2011 w.r.t. 2010.
a)37% Decrease B) 36% Increase c) 31% Decrease d) 41% Decrease
Solution: Using Multiplying Factor Method:
Final Value = 5570
Initial Value = 8820
Mutiplying Factor = Final Value / Initial Value
= 5570 / 8820
= 557 / 882
557/882 can be calculated easily using my previous article
Read: How to calculate Division of two numbers quickly?
Multiplying Factor = 557/882 = 569/900 = 0.6322
% Decrease = (1-0.6322) * 100 = 36.78 %
Hence option A] is correct.