Question

The work done by a man, woman and a child are in the ratio 3:2:1. If daily wages of 20 men, 30 women and 36 children amount to 78/-, what will be the wages of 15 men, 21 women and 30 children for 18 weeks?

• A. 7371/-
• B. 8645/-
• C. 9000/-
• D. 7532/-

Answer 1

The Correct Option is A

To solve this problem, we need to find the daily wages for one man, one woman, and one child based on the given information and then calculate the wages for a specified group over a period of 18 weeks. 

1. First, we know the work done ratio is 3:2:1 for a man, woman, and child, respectively.
2. Let the daily wages for a man, woman, and child be \(3x\), \(2x\), and \(x\), respectively.
3. The total wages for 20 men, 30 women, and 36 children are given as 78/-.
4. Express the total wages equation: \(20 \times 3x + 30 \times 2x + 36 \times x = 78\)
5. Simplify the equation: \(60x + 60x + 36x = 78\)
6. Combine like terms: \(156x = 78\)
7. Solve for \(x\): \(x = \frac{78}{156} = \frac{1}{2}\)
8. Now, calculate the daily wages:
   • Daily wage for one man \(= 3x = 3 \times \frac{1}{2} = \frac{3}{2} = 1.5/-\)
   • Daily wage for one woman \(= 2x = 2 \times \frac{1}{2} = 1/-\)
   • Daily wage for one child \(= x = \frac{1}{2}/-\)
9. Next, calculate the wages for 15 men, 21 women, and 30 children over 18 weeks:
   • Wages for 15 men per day = \(15 \times 1.5 = 22.5/-\)
   • Wages for 21 women per day = \(21 \times 1 = 21/-\)
   • Wages for 30 children per day = \(30 \times 0.5 = 15/-\)
10. Calculate the total daily wages for 15 men, 21 women, and 30 children: \(22.5 + 21 + 15 = 58.5/-\)
11. Over 18 weeks, the total wages becomes: \(58.5 \times 7 \times 18 = 7371/-\)

Thus, the wages for 15 men, 21 women, and 30 children for 18 weeks is 7371/-.