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?

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:

Verification / 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