In a city, 40% of the adults are illiterate while 85% of the children are literate. If the ratio of the adults to that of the children is 2 : 3, then what percent of the population is literate?
Given:
40% of adults are illiterate, so 60% of adults are literate.
85% of children are literate.
Ratio of adults to children = 2:3.
Step 1: Assume Population Proportions
Let the number of adults be 2x and the number of children be 3x.
Step 2: Find Literate People
Literate adults = 60% of \( 2x \) = \( 0.6 \times 2x = 1.2x \).
Literate children = 85% of \( 3x \) = \( 0.85 \times 3x = 2.55x \).
Step 3: Find Total Population and Literate Population
Total population = \( 2x + 3x = 5x \).
Total literate population = \( 1.2x + 2.55x = 3.75x \).
Step 4: Find Percentage of Literate Population
\[
\frac{\text{Total literate population}}{\text{Total population}} \times 100
\]
\[
= \frac{3.75x}{5x} \times 100
\]
\[
= 75\%
\]
Thus, 75% of the total population is literate.
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