The work done by man, a woman and a boy are in the ratio `3 : 2 : 1`. There are 24 men, 20 women and 16 boys in a factory whose weekly wages amount to Rs. 224. What will be the yearly wages of 27 men, 40 women and 15 boys?

Options

A. Rs. 16366
B. Rs. 16466
C. Rs. 16066
D. Rs. 16016

Answer

To solve the problem step by step, we need to find the yearly wages of 27 men, 40 women, and 15 boys based on the given information.

### Step 1: Determine the work done by each individual
The work done by man, woman, and boy is in the ratio of 3:2:1. Let's denote the work done by:
- 1 man = 3x
- 1 woman = 2x
- 1 boy = x

### Step 2: Calculate the total work done by all individuals
Now, we can calculate the total work done by the 24 men, 20 women, and 16 boys:
- Total work done by 24 men = 24 * 3x = 72x
- Total work done by 20 women = 20 * 2x = 40x
- Total work done by 16 boys = 16 * x = 16x

Now, summing these up:
Total work = 72x + 40x + 16x = 128x

### Step 3: Calculate the total wages for the work done
The total weekly wages for all the individuals is Rs. 224. This means that the total work done (128x) corresponds to Rs. 224.
So, we can find the value of x:
\[ 128x = 224 \]
\[ x = \frac{224}{128} = \frac{7}{4} = 1.75 \]

### Step 4: Calculate the individual wages
Now we can calculate the individual wages based on the work done:
- Wage of 1 man = 3x = 3 * 1.75 = Rs. 5.25
- Wage of 1 woman = 2x = 2 * 1.75 = Rs. 3.50
- Wage of 1 boy = x = 1.75

### Step 5: Calculate the yearly wages for 27 men, 40 women, and 15 boys
Now we can calculate the total weekly wages for 27 men, 40 women, and 15 boys:
- Weekly wages for 27 men = 27 * 5.25 = Rs. 141.75
- Weekly wages for 40 women = 40 * 3.50 = Rs. 140
- Weekly wages for 15 boys = 15 * 1.75 = Rs. 26.25

Now, summing these up gives us the total weekly wages:
Total weekly wages = 141.75 + 140 + 26.25 = Rs. 308

### Step 6: Calculate the yearly wages
Since there are 52 weeks in a year, the yearly wages will be:
\[ Yearly wages = 308 * 52 = Rs. 16016 \]

### Final Answer
The yearly wages of 27 men, 40 women, and 15 boys will be Rs. 16016.

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