 # 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 ?

## Question

`A. 50%`
`B. 20%`
`C. 75%`
`D. 25%`

### Solution:

Given:
40% of the adults are illiterate

85% of the children are literate

the ratio of the adults to that of the children is 2 : 3

Formula Used:

%literate population = total literate population/total population × 100

Calculation:

Let the total population be 500

The ratio of the adults to that of the children is 2 : 3

Let the number of adults be 2x and,

Number of children be 3x

⇒ 2x + 3x = 500

⇒ 5x = 500

⇒ x = 500/5

⇒ x = 100

⇒ 2 × 100 = 200

40% of the adults are illiterate

i.e. 60% are literate

⇒ 60/100 × 200

⇒ 120

Out of 200 adults, 120 are literate.

Number of children = 3x

⇒ 3 × 100 = 300

85% of the children are literate.

⇒ 85/100 × 300

⇒ 255

Out of 300 children, 255 are literate.

Total literate = 120 + 255

⇒ Total literate = 375

%literate population = total literate population/total population × 100

⇒ %literate population = 375/500 × 100

⇒ %literate population = 75%

∴ 75% population is literate