Total wages of 3 men, 2 women and 4 boys is Rs 26. If the wages of 3 men is equal to that of 4 women and the wages of 2 women is equal to that of 3 boys, then find out the total wages of 4 men, 3 women and 2 boys.

Options

A. A. 29
B. B. 35
C. C. 65
D. D. 20

Answer

To solve the problem step by step, we will define variables for the wages of men, women, and boys, and then use the relationships given in the question to find the total wages of 4 men, 3 women, and 2 boys.

### Step 1: Define Variables
Let:
- The wage of 1 man = M
- The wage of 1 woman = W
- The wage of 1 boy = B

### Step 2: Write Down the Given Information
From the question, we know:
1. The total wages of 3 men, 2 women, and 4 boys is Rs 26:
\[ 3M + 2W + 4B = 26 \]
2. The wages of 3 men is equal to that of 4 women:
\[ 3M = 4W \quad \text{(1)} \]
3. The wages of 2 women is equal to that of 3 boys:
\[ 2W = 3B \quad \text{(2)} \]

### Step 3: Express W and B in Terms of M
From equation (1):
\[ W = \frac{3M}{4} \]

From equation (2):
\[ B = \frac{2W}{3} = \frac{2 \times \frac{3M}{4}}{3} = \frac{2M}{2} = M \]

### Step 4: Substitute W and B into the Total Wages Equation
Substituting \(W\) and \(B\) into the total wages equation:
\[ 3M + 2\left(\frac{3M}{4}\right) + 4(M) = 26 \]
This simplifies to:
\[ 3M + \frac{6M}{4} + 4M = 26 \]
\[ 3M + 1.5M + 4M = 26 \]
\[ 8.5M = 26 \]

### Step 5: Solve for M
Now, divide both sides by 8.5:
\[ M = \frac{26}{8.5} = \frac{260}{85} = \frac{52}{17} \approx 3.06 \]

### Step 6: Find W and B
Now, substitute \(M\) back to find \(W\) and \(B\):
\[ W = \frac{3M}{4} = \frac{3 \times \frac{52}{17}}{4} = \frac{156}{68} = \frac{39}{17} \approx 2.29 \]
\[ B = M = \frac{52}{17} \approx 3.06 \]

### Step 7: Calculate Total Wages for 4 Men, 3 Women, and 2 Boys
Now we need to find the total wages of 4 men, 3 women, and 2 boys:
\[ \text{Total Wages} = 4M + 3W + 2B \]
Substituting the values:
\[ = 4\left(\frac{52}{17}\right) + 3\left(\frac{39}{17}\right) + 2\left(\frac{52}{17}\right) \]
Combining:
\[ = \frac{208}{17} + \frac{117}{17} + \frac{104}{17} = \frac{429}{17} = 25.24 \]

### Final Answer
Thus, the total wages of 4 men, 3 women, and 2 boys is approximately Rs 29.