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1. Study the following pie-chart and the table given below it carefully to answer the questions given below:
Percentage-wise distribution of lecturers in 6 different subjects in a total number of lecturers: 1600.

Ratio of male to female lecturers

Lecturers Males : Females

Mathematics 3 : 4

Education 5 : 3

Hindi 1 : 3

Chemistry 1 : 7

Physics 9 : 5

Zoology 7 : 9

Total number of lecturers (both male and female) in Hindi is approximately what percent of the total number of female lecturers in Mathematics and chemistry together?

A. 58%

B. 43%

C. 47%

D. 51%

Solution:

Number of lecturers in various subjects are:

\begin{aligned} Chemistry → \frac{13}{100} \times 1600 = 208 \\ Education → \frac{18}{100} \times 1600 = 288 \\ Hindi → \frac{12}{100} \times 1600 = 192 \\ Mathematics → \frac{21}{100} \times 1600 = 336 \\ Physics → \frac{14}{100} \times 1600 = 224 \\ Zoology → \frac{22}{100} \times 1600 = 352 \end{aligned}

Subject	Number of Males	Number of Females
Chemistry	208 × $\frac{1}{8}$ = 26	208 - 26 = 182
Education	288 × $\frac{5}{8}$ = 180	288 - 180 = 108
Hindi	192 × $\frac{1}{4}$ = 48	192 - 48 = 144
Mathematics	336 × $\frac{3}{7}$ = 144	336 - 144 = 192
Physics	224 × $\frac{9}{14}$ = 144	224 - 144 = 80
Zoology	352 × $\frac{7}{16}$ = 154	352 - 154 = 198

\begin{aligned} Required % \\ = (\frac{192}{192 + 182} \times 100) % \\ = (\frac{192}{374} \times 100) % \\ = \frac{9600}{187} % \\ = 51.3 % \\ \approx 51 % \end{aligned}

Lecturers	Males : Females
Mathematics	3 : 4
Education	5 : 3
Hindi	1 : 3
Chemistry	1 : 7
Physics	9 : 5
Zoology	7 : 9

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