The work done by a man, a woman and a child is in the ratio of 3 : 2 : 1. There are 20 men, 30 women and 36 children in a factory. Their weekly wages amount to Rs. 780, which is divided in the ratio of work done by the men, women and children. What will be the wages of 15 men, 21 women and 30 children for 2 weeks?

Options

A. Rs. 585
B. Rs. 292.5
C. Rs. 1170
D. Rs. 900

Answer

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

### Step 1: Determine the work done by each group
The work done by a man, woman, and child is in the ratio of 3:2:1.

Let:
- Work done by 1 man = 3 units
- Work done by 1 woman = 2 units
- Work done by 1 child = 1 unit

### Step 2: Calculate the total work done by each group
Now, we will calculate the total work done by 20 men, 30 women, and 36 children.

- Total work done by 20 men = 20 × 3 = 60 units
- Total work done by 30 women = 30 × 2 = 60 units
- Total work done by 36 children = 36 × 1 = 36 units

### Step 3: Calculate the total work done
Now, we will sum the total work done by all groups:

Total work = Total work by men + Total work by women + Total work by children
= 60 + 60 + 36 = 156 units

### Step 4: Calculate the total ratio of work done
The ratio of work done by men, women, and children is:
- Men: 60 units
- Women: 60 units
- Children: 36 units

To simplify this ratio, we can divide each part by 12:
- Men: 60/12 = 5
- Women: 60/12 = 5
- Children: 36/12 = 3

Thus, the simplified ratio of work done is 5:5:3.

### Step 5: Calculate the total parts in the ratio
Now, we will add the parts of the ratio:
Total parts = 5 + 5 + 3 = 13 parts

### Step 6: Determine the value of one part
The total weekly wages amount to Rs. 780. To find the value of one part, we divide the total wages by the total parts:

Value of one part = Total wages / Total parts
= 780 / 13 = Rs. 60

### Step 7: Calculate the wages for each group
Now, we can calculate the wages for men, women, and children based on the ratio of work done:

- Wages for men = 5 parts × 60 = Rs. 300
- Wages for women = 5 parts × 60 = Rs. 300
- Wages for children = 3 parts × 60 = Rs. 180

### Step 8: Calculate the wages for the specified number of individuals
Next, we will calculate the wages for 15 men, 21 women, and 30 children.

- Wage per man = Total wages for men / Number of men = 300 / 20 = Rs. 15
- Wage per woman = Total wages for women / Number of women = 300 / 30 = Rs. 10
- Wage per child = Total wages for children / Number of children = 180 / 36 = Rs. 5

Now, we calculate the total wages for 15 men, 21 women, and 30 children for 1 week:

- Total wages for 15 men = 15 × 15 = Rs. 225
- Total wages for 21 women = 21 × 10 = Rs. 210
- Total wages for 30 children = 30 × 5 = Rs. 150

### Step 9: Calculate the total wages for one week
Total wages for one week = Wages for men + Wages for women + Wages for children
= 225 + 210 + 150 = Rs. 585

### Step 10: Calculate the total wages for two weeks
Finally, to find the total wages for 2 weeks, we multiply the total wages for one week by 2:

Total wages for 2 weeks = 585 × 2 = Rs. 1170

### Final Answer
The total wages for 15 men, 21 women, and 30 children for 2 weeks is Rs. 1170.

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