In an agricultural village, the ratio of men to women is $5 : 4$. If $60\%$ of the men and $70\%$ of the women are literate, what percentage of the total adult population in the village is literate? ________ % (round off to two decimal places).
Answer Key:
64.44
Step-by-Step Solution & Explanation
**Method 1: Weighted Average Percentage**
Let Men $= 500$ and Women $= 400$. Total population $= 900$.
- Literate men $= 500 \times 0.60 = 300$
- Literate women $= 400 \times 0.70 = 280$
- Total literate $= 300 + 280 = 580$
$\text{Literacy Rate} = \frac{580}{900} \times 100 = \frac{580}{9} = 64.444...\% \approx 64.44\%$
**Method 2: Ratio Weights Formula**
$\text{Overall } \% = \frac{5(60) + 4(70)}{5 + 4} = \frac{300 + 280}{9} = \frac{580}{9} = 64.44\%$