Question

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

Answer 1

Given: 

• Ratio of males to females in the village is 5:4
• Ratio of literate males to literate females is 2:3
• Ratio of illiterate males to illiterate females is 4:3
• Number of literate males = 3600

Step 1: Let the number of males and females in the village be:

• Males = $5x$
• Females = $4x$

Step 2: Literate males and females are in the ratio $2:3$.

Let the common multiple be $y$, then:

• Literate males = $2y$
• Literate females = $3y$

Step 3: Given that literate males = 3600

So, $2y = 3600 \Rightarrow y = 1800$

Thus:

• Literate females = $3 \times 1800 = 5400$

Step 4: Now consider illiterate males and females in the ratio $4:3$.

Let the common multiple be $z$, then:

• Illiterate males = $4z$
• Illiterate females = $3z$

Step 5: Total males = literate males + illiterate males

$5x = 2y + 4z = 3600 + 4z$

Step 6: Total females = literate females + illiterate females

$4x = 3y + 3z = 5400 + 3z$

Now, solve for $x$ using either equation:

From Step 5: $5x = 3600 + 4z \Rightarrow x = \frac{3600 + 4z}{5}$

From Step 6: $4x = 5400 + 3z \Rightarrow x = \frac{5400 + 3z}{4}$

Equating both expressions for $x$:

$\frac{3600 + 4z}{5} = \frac{5400 + 3z}{4}$

Cross-multiply:

$4(3600 + 4z) = 5(5400 + 3z)$

$14400 + 16z = 27000 + 15z$

$16z - 15z = 27000 - 14400$

$z = 12600$

Now find $x$:

$x = \frac{3600 + 4 \times 12600}{5} = \frac{3600 + 50400}{5} = \frac{54000}{5} = 10800$

Total number of females = $4x = 4 \times 10800 = \boxed{43200}$

Answer 2

Given: The ratio of literate males to literate females is 2 : 3.

Number of literate males = 3600

Using the ratio, we calculate the number of literate females:

Literate females = \(\frac{3600}{2} \times 3 = 5400\)

Also given: The male to female ratio in the village is 5 : 4.

Let the total number of males be \(5y\) and total number of females be \(4y\).

Then, illiterate males = \(5y - 3600\)
and illiterate females = \(4y - 5400\)

Given that the ratio of illiterate males to illiterate females is 4 : 3, we write:

\(\frac{5y - 3600}{4y - 5400} = \frac{4}{3}\)

Cross-multiplying:

\(3(5y - 3600) = 4(4y - 5400)\)
\(15y - 10800 = 16y - 21600\)
\(y = 10800\)

Total number of females:

\(4y = 4 \times 10800 = \mathbf{43200}\)

Final Answer: ₹43,200