**Basics:**

Total angle at the center of a pie chart = ${360^0}$

To convert k% percentage into angle = $\displaystyle\frac{k}{{100}} \times {360^0}$

To convert ${m^0}$ into percentage = $\displaystyle\frac{m}{{360}} \times 100$

**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

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% |

Now self employed are ${18^0}$. So self employed as a percentage of employed = $\displaystyle\frac{{18}}{{342}} \times 100 = 5\displaystyle\frac{5}{{19}}\% $

2. Number of persons employed in the Corporate Sector is

a. 250 | b. 500 | c. 750 | d. 1500 |

3. The number of Unemployed persons is

a. 250 | b. 150 | c. 100 | d. 50 |

**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 |

$\displaystyle\frac{{54 + 162}}{{360}} \times 5000 = \displaystyle\frac{{216}}{{360}} \times 5000 = 3000$

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

a. 29% | b. 31 11/19% | c. 34% | d. 31% |

$\displaystyle\frac{{108}}{{342}} \times 100 = \displaystyle\frac{{600}}{{19}} = 31\frac{{11}}{{19}}\% $

**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

a. C

b. F

c. D

d. E

We have to calculate the ratio of Qualified to appeared for each state. So $\displaystyle\frac{\text{Qualified candidates from A}}{\text{Selected candidates from A}} \times 100 = \displaystyle\frac{{18\% \times 9000}}{{15\% \times 45000}} \times 100$

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 |

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 |

Appeared candidates from B and C = (11 + 8)% = 19% (45000)

So required percentage = $\displaystyle\frac{{23\% (9000)}}{{19\% (45000)}} \times 100 = \displaystyle\frac{{23}}{{19 \times 5}} \times 100 = 24.21$

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 |