In a village, 5/8 of the population are adults. Half of the adults are males, and 4/5 of the adult females are illiterate. If the number of illiterate adult females is 400, what is the total population of the village?
Aptitude
Decimal Fraction
Difficulty: Easy
Choose an option
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A2000
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B1500
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C1800
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D1600
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E1750
Answer
Correct Answer: 1600
Explanation
Introduction / Context:This problem chains several fractions to determine a whole population from a known sub-group count. It assesses careful fraction handling and back-calculation from a part to the total.
Given Data / Assumptions:
- Total population = P.
- Adults = (5/8)P.
- Adult males = half of adults; therefore adult females = half of adults = (1/2)*(5/8)P = (5/16)P.
- Illiterate adult females = (4/5) of adult females = 400.
Concept / Approach:First express the number of adult females as a fraction of P. Then use the given count of illiterate adult females (a fraction of those adult females) to solve for P.
Step-by-Step Solution:
Adult females = (5/16)PIlliterate adult females = (4/5) * (5/16)P = (20/16)P = (5/4)PBut this equals 400, so (4/5) * (5/16)P = 400 → (1/4)P = 100 → P = 400 * (16/5)Compute directly: (4/5)*(5/16)P = 400 ⇒ (1/4)P = 400 ⇒ P = 1600Verification / Alternative check:Adult females = (5/16)*1600 = 500; 4/5 of 500 = 400. Matches the given number.
Why Other Options Are Wrong:
- 2000, 1500, 1800, 1750: None satisfy both the adult-fraction and the illiteracy fraction when checked.
Common Pitfalls:
- Mistaking adult females as 5/8 rather than 5/16 of the population.
- Arithmetic slips with compound fractions.
Final Answer:1600