In a village there are ` 60%` males and rest are females `30%` of total male are illiterate and `25%` of total female are illiterate . Number of illiterate males is 1152
Quantity I. Literate females in the village
Quantity II. 1940

Options

A. If Quantity I ` gt` Quantity II
B. If Quantity I ` lt` Quantity II
C. If Quantity I ` ge` Quantity II
D. If Quantity I ` le` Quantity II

Answer

To solve the problem step by step, we will first determine the total population of the village, then calculate the number of literate females based on the information provided.

### Step 1: Determine the total number of males in the village.
Let the total population of the village be \( P \).

Since 60% of the population are males:
\[ \text{Number of males} = 0.6P \]

### Step 2: Calculate the number of illiterate males.
We know that 30% of the total males are illiterate, and the number of illiterate males is given as 1152.
\[ \text{Illiterate males} = 0.3 \times \text{Number of males} = 1152 \]
Substituting the number of males:
\[ 0.3 \times (0.6P) = 1152 \]
\[ 0.18P = 1152 \]

### Step 3: Solve for \( P \).
To find \( P \), divide both sides by 0.18:
\[ P = \frac{1152}{0.18} = 6400 \]

### Step 4: Calculate the number of females in the village.
Since the total population \( P \) is 6400 and 60% are males, the number of females is:
\[ \text{Number of females} = P - \text{Number of males} = 6400 - 0.6 \times 6400 = 6400 - 3840 = 2560 \]

### Step 5: Calculate the number of illiterate females.
We know that 25% of the total females are illiterate:
\[ \text{Illiterate females} = 0.25 \times \text{Number of females} = 0.25 \times 2560 = 640 \]

### Step 6: Calculate the number of literate females.
The number of literate females can be calculated by subtracting the number of illiterate females from the total number of females:
\[ \text{Literate females} = \text{Number of females} - \text{Illiterate females} = 2560 - 640 = 1920 \]

### Step 7: Compare with Quantity II.
Now we compare the number of literate females (1920) with Quantity II (1940):
- Quantity I: 1920
- Quantity II: 1940

Since 1920 < 1940, we conclude that Quantity I is less than Quantity II.

### Final Answer:
**Quantity I is less than Quantity II.**

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