Forty per cent of the employees of a certain company are men, and 75% of the men earn more than Rs. 38,000 per year. If 48% of the company's employees earn more than Rs. 38,000 per year, what fraction of the women employed by the company earn less than or equal to Rs. 38,000 per year?

Options

A. `(2)/(3)`
B. `(4)/(5)`
C. `(3)/(4)`
D. `(7)/(10)`

Answer

To solve the problem step by step, we will first define the total number of employees and then calculate the number of men and women, followed by the number of employees earning more than Rs. 38,000.

### Step 1: Define the total number of employees
Assume the total number of employees in the company is 100.

### Step 2: Calculate the number of men and women
Since 40% of the employees are men:
- Number of men = 40% of 100 = 40 men
- Number of women = 100 - 40 = 60 women

### Step 3: Calculate the number of men earning more than Rs. 38,000
75% of the men earn more than Rs. 38,000:
- Number of men earning more than Rs. 38,000 = 75% of 40 = 0.75 × 40 = 30 men

### Step 4: Calculate the total number of employees earning more than Rs. 38,000
It is given that 48% of the company's employees earn more than Rs. 38,000:
- Total employees earning more than Rs. 38,000 = 48% of 100 = 48 employees

### Step 5: Calculate the number of women earning more than Rs. 38,000
We already know the number of men earning more than Rs. 38,000 (30 men). Therefore, the number of women earning more than Rs. 38,000 can be calculated as follows:
- Number of women earning more than Rs. 38,000 = Total earning more than Rs. 38,000 - Number of men earning more than Rs. 38,000
- Number of women earning more than Rs. 38,000 = 48 - 30 = 18 women

### Step 6: Calculate the number of women earning less than or equal to Rs. 38,000
To find the number of women earning less than or equal to Rs. 38,000, we subtract the number of women earning more than Rs. 38,000 from the total number of women:
- Number of women earning less than or equal to Rs. 38,000 = Total women - Number of women earning more than Rs. 38,000
- Number of women earning less than or equal to Rs. 38,000 = 60 - 18 = 42 women

### Step 7: Calculate the fraction of women earning less than or equal to Rs. 38,000
The fraction of women earning less than or equal to Rs. 38,000 is given by:
- Fraction = Number of women earning less than or equal to Rs. 38,000 / Total number of women
- Fraction = 42 / 60 = 7 / 10

### Final Answer:
The fraction of the women employed by the company who earn less than or equal to Rs. 38,000 per year is **7/10**.

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