The work done by a man, a woman and a child are in the ratio 3:2:1. If the daily wages of 20 men, 30 women and 36 children amount to ₹ 78, what will be the wages of 15 men, 21 women and 30 children for 18 weeks?

Options

A. ₹ `7371`
B. ₹ `8645`
C. ₹ `9000`
D. 9500

Answer

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

### Step 1: Understand the Work Ratio
The work done by a man, a woman, and a child is in the ratio of 3:2:1. This means:
- Work done by 1 man = 3 units
- Work done by 1 woman = 2 units
- Work done by 1 child = 1 unit

### Step 2: Calculate Total Work Units for 20 Men, 30 Women, and 36 Children
We can express the work done by each group in terms of units:
- Work done by 20 men = 20 * 3 = 60 units
- Work done by 30 women = 30 * 2 = 60 units
- Work done by 36 children = 36 * 1 = 36 units

Now, we sum these up:
Total work = 60 + 60 + 36 = 156 units

### Step 3: Determine the Daily Wages per Unit of Work
According to the problem, the total daily wages for 20 men, 30 women, and 36 children is ₹78.
Thus, the wage per unit of work can be calculated as:
\[ \text{Wage per unit} = \frac{78}{156} = 0.5 \text{ (₹ per unit)} \]

### Step 4: Calculate the Work Done by 15 Men, 21 Women, and 30 Children
Next, we calculate the total work done by 15 men, 21 women, and 30 children:
- Work done by 15 men = 15 * 3 = 45 units
- Work done by 21 women = 21 * 2 = 42 units
- Work done by 30 children = 30 * 1 = 30 units

Now, we sum these up:
Total work = 45 + 42 + 30 = 117 units

### Step 5: Calculate Daily Wages for 117 Units of Work
Now, we can find the daily wages for 117 units of work:
\[ \text{Daily wages} = 117 \times 0.5 = 58.5 \text{ (₹)} \]

### Step 6: Calculate Total Wages for 18 Weeks
To find the total wages for 18 weeks, we first need to calculate the total number of days in 18 weeks:
\[ \text{Total days} = 18 \times 7 = 126 \text{ days} \]

Now, we can calculate the total wages for 126 days:
\[ \text{Total wages} = 58.5 \times 126 = 7371 \text{ (₹)} \]

### Final Answer
The total wages for 15 men, 21 women, and 30 children for 18 weeks is ₹7371.

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