CLAT 2020 Quantitative Techniques: Japanese Encephalitis

The following data presents the cases of Japanese Encephalitis in five states of India

By what percentage is the average of males in Chhattisgarh, Jharkhand and Andhra Pradesh together more or less than the average of females in West Bengal, Jharkhand and Odisha together who are affected by Japanese encephalitis?

Number of males affected in a state \(=\frac{\text { ratio of males }}{\text { total ratio }} \times \text { Total number of people effected by encephalitis in a particular state }\)
Number of males affected in Chattisgarh \(=\frac{5}{7} \times 21000=15000\)
Number of males affected in Jharkhand \(=\frac{15}{29} \times 29000=15000\)
Number of males affected in Andhra Pradesh \(=\frac{7}{13} \times 13000=7000\)

The average number of males affected in these 3 states \(=\frac{(15000+15000+7000)}{3}=12,333 (approx.)\)

Number of females affected in a state \(=\frac{\text { ratio of females }}{\text { total ratio }} \times \text { Total number of people effected by encephalitis in a particular state }\)
Number of females affected in Odisha \(=\frac{7}{19} \times 57000=21000\)
Number of females affected in West Bengal \(=\frac{3}{9} \times 45000=15000\) 
Number of females affected in Jharkhand \(=\frac{14}{29} \times 29000=14000\)

The average number of females affected in these 3 states \(=\frac{(21000+15000+14000)}{3}=16,666 (approx.)\)

Comparing the two numbers, \(\frac{(12333)}{16333} = 0.74\) (approx.).
That means the average number of males affected in Chattisgarh, Jharkhand, and Andhra Pradesh is 26% less than the females affected in Odisha, West Bengal, and Jharkhand.

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