A company employs skilled workers, unskilled workers, and clerks in the proportion of 8 : 5: 1, and the wage of a skilled worker, an unskilled worker, and a clerk are in the ratio of 5: 2 : 3. When 20 unskilled workers are employed, the total daily wages all amount to Rs. 3180. Find the daily wages paid to each category of employees.
Question
A company employs skilled workers, unskilled workers, and clerks in the proportion of 8 : 5: 1, and the wage of a skilled worker, an unskilled worker, and a clerk are in the ratio of 5: 2 : 3. When 20 unskilled workers are employed, the total daily wages all amount to Rs. 3180. Find the daily wages paid to each category of employees.
Solution
Step 1: Understand the problem
The problem gives us two ratios. The first ratio is the proportion of skilled workers, unskilled workers, and clerks in the company, which is 8:5:1. The second ratio is the wage of a skilled worker, an unskilled worker, and a clerk, which is 5:2:3.
We also know that when 20 unskilled workers are employed, the total daily wages amount to Rs. 3180.
Step 2: Find the wage of an unskilled worker
We know that the total daily wages when 20 unskilled workers are employed is Rs. 3180. So, the wage of one unskilled worker is Rs. 3180 / 20 = Rs. 159.
Step 3: Find the wage of a skilled worker and a clerk
We know that the wage of a skilled worker, an unskilled worker, and a clerk are in the ratio of 5:2:3. So, the wage of a skilled worker is (5/2) * Rs. 159 = Rs. 397.5 and the wage of a clerk is (3/2) * Rs. 159 = Rs. 238.5.
Step 4: Find the total daily wages paid to each category of employees
We know that the company employs skilled workers, unskilled workers, and clerks in the proportion of 8:5:1. So, the total daily wages paid to skilled workers is 8 * Rs. 397.5 = Rs. 3180, to unskilled workers is 5 * Rs. 159 = Rs. 795, and to clerks is 1 * Rs. 238.5 = Rs. 238.5.
So, the daily wages paid to skilled workers, unskilled workers, and clerks are Rs. 3180, Rs. 795, and Rs. 238.5 respectively.
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