Wages of 45 women for 30 days amount to ? 31050. How many men must work for 10 days to receive ? 11500, if the daily wages of a man being double those of a woman?

Options

A. a.25
B. b.20
C. c.30
D. d.none of these

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the Daily Wage of a Woman
We know that the wages of 45 women for 30 days amount to ₹31,050. We can use the formula:

\[ \text{Total Wages} = \text{Number of Women} \times \text{Daily Wage of Woman} \times \text{Number of Days} \]

Substituting the known values:

\[ 31,050 = 45 \times \text{Daily Wage of Woman} \times 30 \]

Now, we can isolate the Daily Wage of a Woman:

\[ \text{Daily Wage of Woman} = \frac{31,050}{45 \times 30} \]

Calculating the right side:

\[ \text{Daily Wage of Woman} = \frac{31,050}{1350} = 23 \]

### Step 2: Calculate the Daily Wage of a Man
According to the problem, the daily wage of a man is double that of a woman:

\[ \text{Daily Wage of Man} = 2 \times \text{Daily Wage of Woman} = 2 \times 23 = 46 \]

### Step 3: Set Up the Equation for Men
We need to find out how many men must work for 10 days to receive ₹11,500. We can set up the equation similarly:

\[ \text{Total Wages} = \text{Number of Men} \times \text{Daily Wage of Man} \times \text{Number of Days} \]

Substituting the known values:

\[ 11,500 = \text{Number of Men} \times 46 \times 10 \]

### Step 4: Isolate the Number of Men
Now we can isolate the Number of Men:

\[ \text{Number of Men} = \frac{11,500}{46 \times 10} \]

Calculating the right side:

\[ \text{Number of Men} = \frac{11,500}{460} = 25 \]

### Final Answer
Thus, the number of men required to work for 10 days to receive ₹11,500 is **25**.

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