Direction : Table given below shows percentage of total literate population of…
2020
Direction : Table given below shows percentage of total literate population of five (A, B, C, D & E) villages, literate male, illiterate male and total female (literate + illiterate). Read the data carefully and answer the questions.
Note - 'NA' means some values are missing which you have to calculate if required.
If the number of female graduates in village C is equal to the number of illiterate males in village C and the difference between the number of graduate female and under graduate female in village C is 120, then find the total population of village C (Note – There is only graduate and under graduate population in village C)?
- A.
4000
- B.
2000
- C.
1250
- D.
3000
- E.
2500
Show answer & explanation
Correct answer: E
Concept: In such literacy tables, a person can be a graduate or an undergraduate only if they are literate — an illiterate person is neither. So when a village is described as having only graduate and undergraduate population, that split applies to the literate group. The female literates therefore divide exactly into female graduates and female undergraduates, and Total literate = Male literate + Female literate, while Total illiterate = Total population − Total literate.
Application (village C): Let the total population be P.
Literate population = 80% of P = 0.80P, so Illiterate population = 20% of P = 0.20P.
Male illiterate = 60% of total illiterate = 0.60 × 0.20P = 0.12P.
Female literate = Total literate − Male literate = 0.80P − 1280.
Female graduates = Male illiterates = 0.12P (given).
Female undergraduates = Female literate − Female graduates = (0.80P − 1280) − 0.12P = 0.68P − 1280.
Difference between undergraduate and graduate females = (0.68P − 1280) − 0.12P = 0.56P − 1280, and this is given as 120.
0.56P − 1280 = 120 → 0.56P = 1400 → P = 2500.
Cross-check: With P = 2500: literate = 2000, illiterate = 500, male illiterate = 300, so female graduates = 300. Female literate = 2000 − 1280 = 720, so female undergraduates = 720 − 300 = 420. The difference 420 − 300 = 120 matches the condition exactly, and graduates + undergraduates = 720 equals the female literate count, so the population total of 2500 is consistent.