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?

The correct answer is 26% (Option 3).

From the given bar chart and table in the image, we have the total number of persons affected by Japanese encephalitis (in thousands) and the ratio of Male to Female for each state as follows:

1. Odisha: Total = 57, Male : Female = 12 : 7
2. West Bengal: Total = 45, Male : Female = 6 : 3 (which simplifies to 2 : 1)
3. Chhattisgarh: Total = 21, Male : Female = 5 : 2
4. Jharkhand: Total = 29, Male : Female = 15 : 14
5. Andhra Pradesh: Total = 13, Male : Female = 7 : 6

Step 1: Calculate the number of affected males in Chhattisgarh, Jharkhand, and Andhra Pradesh.

• Chhattisgarh:
Males = $\frac{5}{5+2}\times 21=\frac{5}{7}\times 21=15$ thousand.

• Jharkhand:
Males = $\frac{15}{15+14}\times 29=\frac{15}{29}\times 29=15$ thousand.

• Andhra Pradesh:
Males = $\frac{7}{7+6}\times 13=\frac{7}{13}\times 13=7$ thousand.

Total males in Chhattisgarh, Jharkhand, and Andhra Pradesh = 15 + 15 + 7 = 37 thousand.
Average of males in these three states = $\frac{37}{3}$ thousand.

Step 2: Calculate the number of affected females in West Bengal, Jharkhand, and Odisha.

• West Bengal:
Females = $\frac{3}{6+3}\times 45=\frac{3}{9}\times 45=15$ thousand.

• Jharkhand:
Females = $\frac{14}{15+14}\times 29=\frac{14}{29}\times 29=14$ thousand.

• Odisha:
Females = $\frac{7}{12+7}\times 57=\frac{7}{19}\times 57=21$ thousand.

Total females in West Bengal, Jharkhand, and Odisha = 15 + 14 + 21 = 50 thousand.
Average of females in these three states = $\frac{50}{3}$ thousand.

Step 3: Calculate the percentage difference.

Difference in averages = $\frac{50}{3}-\frac{37}{3}=\frac{13}{3}$ thousand.

Percentage by which the male average is less than the female average:

$\text{Percentage}=\frac{\frac{13}{3}}{\frac{50}{3}}\times 100=\frac{13}{50}\times 100=26\%$

Therefore, the average of males in Chhattisgarh, Jharkhand, and Andhra Pradesh together is 26% less than the average of females in West Bengal, Jharkhand, and Odisha together.