The total number of men, women and children working in a factory is 18. They earn ₹ 4000 in a day. If the sum of the wages of all men, all women and all children is in the ratio of 18 : 10 : 12 and if the wages of an individual man, woman and child is in the ratio 6 : 5 : 3, then how. much a woman earn in a day?

Options

A. ₹ 400
B. ₹ 250
C. ₹ 150
D. ₹ 120

Answer

To solve the problem step by step, we will break down the information given and use it to find out how much a woman earns in a day.

### Step 1: Understand the Ratios
We are given two sets of ratios:
1. The total wages of men, women, and children are in the ratio of 18:10:12.
2. The wages of an individual man, woman, and child are in the ratio of 6:5:3.

### Step 2: Calculate Total Units of Wages
From the first ratio (18:10:12), we can find the total units:
- Total units = 18 + 10 + 12 = 40 units.

### Step 3: Calculate the Value of Each Unit
The total earnings per day are ₹4000. Therefore, the value of each unit is:
- Value of each unit = Total earnings / Total units = ₹4000 / 40 = ₹100.

### Step 4: Calculate Total Wages for Each Group
Now, we can calculate the total wages for men, women, and children:
- Total wages for men = 18 units × ₹100 = ₹1800.
- Total wages for women = 10 units × ₹100 = ₹1000.
- Total wages for children = 12 units × ₹100 = ₹1200.

### Step 5: Understand Individual Wages
Next, we look at the second ratio (6:5:3) for individual wages:
- Total parts = 6 + 5 + 3 = 14 parts.

### Step 6: Calculate the Value of Each Individual Wage Unit
To find the value of each part for individual wages, we need to divide the total wages of each group by their respective ratios:
- Total earnings of men = ₹1800.
- Total earnings of women = ₹1000.
- Total earnings of children = ₹1200.

### Step 7: Calculate Individual Wages
Now, we can calculate the individual wages:
- Value of each part for men = ₹1800 / 6 = ₹300.
- Value of each part for women = ₹1000 / 5 = ₹200.
- Value of each part for children = ₹1200 / 3 = ₹400.

### Step 8: Find the Earnings of a Woman
From the calculations above, we find that:
- Each woman earns ₹200 per day.

### Final Answer
Thus, the amount a woman earns in a day is **₹200**.

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