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Men, women and children are employed to do a work in the proportion of 3 : 2 : 1 and their wages as 5:3:2. When 90 men are employed, total daily wages of all amounts to ? 10350. Find the daily wages of a man.

A

1) 45`

B

2) 57.50`

C

3)115`

D

4) 75`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we will follow the given information about the proportions of men, women, and children, as well as their wages. ### Step 1: Understand the Proportions The problem states that men, women, and children are employed in the ratio of 3:2:1. This means for every 3 men, there are 2 women and 1 child. ### Step 2: Assign Variables Let: - The number of men = 3x - The number of women = 2x - The number of children = x ### Step 3: Total Number of Workers According to the problem, when 90 men are employed, we can set up the equation: \[ 3x = 90 \] From this, we can solve for \( x \): \[ x = \frac{90}{3} = 30 \] ### Step 4: Calculate the Number of Women and Children Now we can find the number of women and children: - Number of women = \( 2x = 2 \times 30 = 60 \) - Number of children = \( x = 30 \) ### Step 5: Understand the Wages Proportions The wages are given in the ratio of 5:3:2 for men, women, and children respectively. This means: - Wages of a man = 5y - Wages of a woman = 3y - Wages of a child = 2y ### Step 6: Total Wages Calculation Now, we can calculate the total wages paid to all workers: Total wages = (Number of men × Wages of a man) + (Number of women × Wages of a woman) + (Number of children × Wages of a child) Substituting the values: \[ \text{Total wages} = (90 \times 5y) + (60 \times 3y) + (30 \times 2y) \] \[ = 450y + 180y + 60y \] \[ = 690y \] ### Step 7: Set Up the Equation We know from the problem that the total daily wages amount to 10,350: \[ 690y = 10,350 \] ### Step 8: Solve for y Now, we can solve for \( y \): \[ y = \frac{10,350}{690} \] \[ y = 15 \] ### Step 9: Calculate Daily Wages of a Man Now that we have the value of \( y \), we can find the daily wages of a man: \[ \text{Wages of a man} = 5y = 5 \times 15 = 75 \] ### Final Answer The daily wages of a man are **75 rupees**. ---
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