Arithmetic

Ratio, Proportion & Variation

Hard

In a village, the ratio of number of males to females is $5: 4$ . The ratio of number of literate males to literate females is $2 : 3$ . The ratio of the number of illiterate males to illiterate females is $4: 3$ . If $3600$ males in the village are literate, then the total number of females in the village is

Entered answer:

✅ Correct Answer: 43200

We have a village with specific ratios between different groups:

Overall ratio: Males : Females = 5 : 4

Literate ratio: Literate males : Literate females = 2 : 3

Illiterate ratio: Illiterate males : Illiterate females = 4 : 3

Given fact: 3600 males are literate

Since we're dealing with ratios, let's use variables to represent the actual numbers:

For the overall population:

Total males = 5k (where k is our scaling factor)

Total females = 4k

For literate people:

Literate males = 2x (where x is our scaling factor for literacy)

Literate females = 3x

For illiterate people:

Illiterate males = 4y (where y is our scaling factor for illiteracy)

Illiterate females = 3y

We know that 3600 males are literate, so:

Literate males = 2x = 3600

Therefore: x = 3600 ÷ 2 = 1800

Now we can find:

Literate females = 3x = 3(1800) = 5400

Here's the crucial part: Every male is either literate or illiterate (no other category exists).

This means:

Total males = Literate males + Illiterate males

5k = 2x + 4y

Similarly:

Total females = Literate females + Illiterate females

4k = 3x + 3y

Since the overall ratio of males to females is 5:4, we can write:

$\tfrac{\text{Total males}}{\text{Total females}} = \tfrac{5k}{4k} = \tfrac{5}{4}$

Substituting our expressions:

$\tfrac{2x + 4y}{3x + 3y} = \tfrac{5}{4}$

$4(2x + 4y) = 5(3x + 3y)$

$8x + 16y = 15x + 15y$

$16y - 15y = 15x - 8x$

$y = 7x$

Since x = 1800:

$y = 7(1800) = 12600$

Total females in the village = Literate females + Illiterate females

$= 3x + 3y$

$= 3(1800) + 3(12600)$

$= 5400 + 37800$

$= 43200$

Therefore, the total number of females in the village is 43200.

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