The following data presents the cases of Japanese Encephalitis in five states of India
Question: 1
Number of females affected by Japanese encephalitis in West Bengal are what percentage (up to 1 decimal) more or less than that of females affected in Odisha?
This question compares the number of females affected by Japanese encephalitis in West Bengal with the number in Odisha, using the total cases and the male to female ratio given for each state. Let's work out the actual numbers first and then match them against the options.
28.6% less: Odisha recorded 57 thousand total cases in a male to female ratio of 12:7, which splits into 19 equal parts of 3 thousand each, giving 36 thousand males and 21 thousand females. West Bengal recorded 45 thousand total cases in a ratio of 6:3, the same as 2:1, which splits into 3 equal parts of 15 thousand each, giving 30 thousand males and 15 thousand females. The shortfall of West Bengal's females compared to Odisha's is 21 minus 15, which is 6 thousand. As a percentage of Odisha's 21 thousand females, that is 6 divided by 21, which works out to about 28.6%, so West Bengal's female count is 28.6% less than Odisha's. This matches the computed figure exactly.
29.7% more: This would only be correct if West Bengal's female count exceeded Odisha's, but 15 thousand is clearly lower than 21 thousand, so a "more" figure cannot be right here.
26.8% less: This is close to the correct percentage but does not match the exact calculation of 6 out of 21, which rounds to 28.6%, not 26.8%.
25.8% more: Like the second option, this direction is wrong since West Bengal's females are fewer than Odisha's, not more, so this cannot be correct either.
Working out the actual female counts for both states shows West Bengal's figure is lower, and the shortfall comes out to exactly 28.6% of Odisha's count.
Therefore, the correct answer is 28.6% less.
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Question: 2
What is the average number of males affected by Japanese encephalitis in all the five states?
This question asks for the average number of males affected by Japanese encephalitis across all five states, using the total cases and the male to female ratios given for each state. We first need the male count in every state before we can average them.
9,000: This figure is far too low. Even a single state like Odisha alone has 36 thousand males affected, so an average across five states cannot fall this low.
13,500: This is still below the true average, since the male counts in the larger states, Odisha and West Bengal, alone push the total well past what this average would allow.
18,400: This is closer to the correct range but still short of the actual figure once every state's male count is added up correctly.
20,600: Splitting each state's total by its given ratio gives males of 36 thousand in Odisha, 30 thousand in West Bengal, 15 thousand in Chhattisgarh, 15 thousand in Jharkhand, and 7 thousand in Andhra Pradesh. Adding these gives 36 + 30 + 15 + 15 + 7 = 103 thousand males in total. Dividing by the 5 states gives 103,000 divided by 5, which is exactly 20,600. This matches the computed average precisely.
Only after breaking each state's total into its male and female parts using the given ratios, and summing the male parts, does the true average become clear.
Therefore, the correct answer is 20,600.
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Question: 3
If the total number of males affected by Japanese Encephalitis in other states are 87 % more than the average number of males in Odisha, West Bengal, Chhattisgarh and Jharkhand, the total number of males affected in India is:
This question builds on the male counts for four of the five states, Odisha, West Bengal, Chhattisgarh, and Jharkhand, to work out the number of males affected in the rest of the country, and then the total for all of India. Let's calculate this step by step and check it against the options.
44,880: This is the number of males affected in the "other states" alone, worked out as 87% more than the average of the four states. It is not the total for the whole of India, only one part of it, so this cannot be the final answer even though it is a correct intermediate figure.
1,40,880: The average of the male counts in Odisha, West Bengal, Chhattisgarh, and Jharkhand is (36 + 30 + 15 + 15) divided by 4, which is 96 divided by 4, giving 24 thousand. A figure 87% more than this average is 24 multiplied by 1.87, which comes to 44.88 thousand, or 44,880. Adding this to the combined total of the four states, 96,000, gives 96,000 plus 44,880, which is 1,40,880. This matches the total worked out in full.
1,47,880: This figure would only appear if all five states, including Andhra Pradesh, were added into the base total before adding the "other states" figure, which goes beyond what this particular question is asking for.
68,880: This does not correspond to any consistent combination of the average and the four state totals, and is too far from the correctly worked out figure to be right.
Adding the male counts of the four named states to the separately calculated "other states" figure gives the complete total asked for in the question.
Therefore, the correct answer is 1,40,880.
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Question: 4
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?
This question compares two separate averages built from the state data: the average number of males in Chhattisgarh, Jharkhand, and Andhra Pradesh, against the average number of females in West Bengal, Jharkhand, and Odisha. Let's compute both averages and then find the percentage difference.
22: This is lower than the actual percentage difference once both averages are worked out precisely, so it does not match.
24: This is closer to the true value but still falls short of the exact figure obtained from the calculation.
26: The male average is (15 + 15 + 7) divided by 3, which is 37 divided by 3, or about 12.33 thousand. The female average is (15 + 14 + 21) divided by 3, which is 50 divided by 3, or about 16.67 thousand. The male average is smaller, and the shortfall is 16.67 minus 12.33, which is 4.33. As a percentage of the female average, 4.33 divided by 16.67 comes to almost exactly 26%. This matches the computed difference.
28: This overshoots the actual computed percentage difference and does not match the precise averages worked out from the data.
Once both three state averages are calculated correctly, the male average turns out to be about 26% lower than the female average.
Therefore, the correct answer is 26.
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Question: 5
What is the percentage (up to 1 decimal) of females affected by ‘Japanese encephalitis’ of the total affected population across five states?
This question asks what percentage of the total affected population, across all five states combined, is made up of females. We need the total number of females and the grand total of everyone affected.
25.4: This is well below the actual share of females once the totals are added up correctly.
36.7: This is close to the correct figure but does not match the precise calculation.
24.5: Like the first option, this underestimates the true female share by a wide margin.
37.6: Adding the female counts across all five states gives 21 + 15 + 6 + 14 + 6, which is 62 thousand. The grand total across all states, both males and females, is 57 + 45 + 21 + 29 + 13, which is 165 thousand. Females as a percentage of this total are 62 divided by 165, multiplied by 100, which comes to about 37.6%. This matches the calculation exactly.
Working out the combined female count and the combined overall total, then taking their ratio, gives the correct share.
