DATA INTERPRETATION ( PIE CHARTS)

Basics:  
Total angle at the center of a pie chart = 3600${360}^0$
To convert k% percentage into angle = k100×3600${\displaystyle \frac{k}{100}\times {360}^0}$
To convert m0$m^0$ into percentage = m360×100${\displaystyle \frac{m}{360}\times 100}$

Set 1 : The various sections of the population are indicated below in the pie-chart. Study the pie-chart and answer the following questions:

The total population of a city is 5000

I.  Employees of the Public Sector II. Employees of the Private Sector
III. Employees of the Corporate Sector IV. Self-Employed    V. Unemployed.

1. What percentage of the employed persons is self employed?

a.   5%

b.  5 5/19 %

c.  19%

d.  20%

Solution:  Total Employed = Total population - Unemployed = 3600−180=3420${360}^0-{18}^0={342}^0$
Now self employed are 180${18}^0$. So self employed as a percentage of employed = 18342×100=5519%${\displaystyle \frac{18}{342}\times 100=5{\displaystyle \frac{5}{19}\mathrm{\%}}}$

2. Number of persons employed in the Corporate Sector is 

a.   250

b.  500

c.  750

d.  1500

Solution: We have to convert degrees into numbers.  So 54360×5000=750${\displaystyle \frac{54}{360}\times 5000=750}$

3. The number of Unemployed persons is 

a.   250

b.  150

c.  100

d.  50

Solution: We have to convert degrees into numbers. So 18360×5000=250${\displaystyle \frac{18}{360}\times 5000=250}$
Shortcut: We calculated corporate sector employees as 750. But from pie chart Corporate sector employees are 3 times of unemployed. So 1/3rd of 750 = 250

4. The number of persons employed in both the Public Sector and Corporate Sector is 

a.   3750

b.  3000

c.  2500

d.  2200

Solution: Number of persons employed in public sector and corporate sector together = 54 + 162 = 216.
54+162360×5000=216360×5000=3000${\displaystyle \frac{54+162}{360}\times 5000={\displaystyle \frac{216}{360}\times 5000=3000}}$

5. What percentage of the employed persons is employed in Private Sector ?

a.   29%

b.  31 11/19%

c.  34%

d.  31%

From the 1st question, employed are 342. and From pie chart private sector employees are 108.
108342×100=60019=311119%${\displaystyle \frac{108}{342}\times 100={\displaystyle \frac{600}{19}=31\frac{11}{19}\mathrm{\%}}}$

Set 2:  These questions are based on following graphs Classification of appeared candidates in a competitive test from different states and qualified candidates from those states.

1. What is the ratio between the number of appeared candidates from states C and E together and the appeared candidates from states A and F together ?
a.  17 : 33
b.  11 : 13
c.  13 : 27
d.  17 : 27 
Solution: There is not need to calculate values. This is simply a ratio. So we can compare the ratio of their percentages. C + E = 8 + 9 = 17; A + F = 15 + 18 = 33.

So ratio = 17 : 33
2. In which State the percentage of qualified candidates to that of appeared candidates is minimum ?

a.  C

b.  F

c.  D

d.  E

Solution:  This is a lengthy question. But we will use simple technique to solve this question.
We have to calculate the ratio of Qualified to appeared for each state. So Qualified candidates from ASelected candidates from A×100=18%×900015%×45000×100${\displaystyle \frac{\text{Qualified candidates from A}}{\text{Selected candidates from A}}\times 100={\displaystyle \frac{18\mathrm{\%}\times 9000}{15\mathrm{\%}\times 45000}\times 100}}$
But If you observe in the above equation, only 18% / 15% changes for each state. Remaining values are constant. Minimum percentage we get if numerator is small and denominator is big.
For C it is 7/8 = 1/1.14 and for E it is 9/14 = 1/1.5 So for E denominator is big. So it has the ratio Minimum.
So Option D is correct.

3. What is the difference between the number of qualified candidates of states D and G

a.   690

b.  670

c.  780

d.  720

Solution: Instead of calculating qualified candidates for D and G separately, we take the difference in their percentages.  i.e., 8% (9000) = 720.

4. What is the percentage of qualified candidates to that of appeared candidates from states B and C taken together ?

a.   23.11

b.  24.21

c.  21.24

d.  23

Qualified candidates from B and C = (16 + 7)% = 23% (9000)
Appeared candidates from B and C = (11 + 8)% = 19% (45000)
So required percentage = 23%(9000)19%(45000)×100=2319×5×100=24.21${\displaystyle \frac{23\mathrm{\%}(9000)}{19\mathrm{\%}(45000)}\times 100={\displaystyle \frac{23}{19\times 5}\times 100=24.21}}$

5. What is the ratio between number of candidates qualified from states B and D together and the number of candidates appeared from state C respectively ?

a.   8 : 37

b.  11 : 12

c.  37 : 48

d.  7 : 37

Solution: The required ration = (16 + 21)% (9000) : 8% (45000) ⇒$\Rightarrow$ 37 : 8 x 5 ⇒$\Rightarrow$ 37 : 40