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.Rs. 2100, Rs. 800, Rs. 280Rs. 2400, Rs. 480, Rs. 300Rs. 2400, Rs. 600, Rs. 180Rs. 2200, Rs. 560, Rs. 420
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.Rs. 2100, Rs. 800, Rs. 280Rs. 2400, Rs. 480, Rs. 300Rs. 2400, Rs. 600, Rs. 180Rs. 2200, Rs. 560, Rs. 420
Solution
Let's solve this step by step:
Step 1: We know that the ratio of skilled workers, unskilled workers, and clerks is 8:5:1. So, if there are 20 unskilled workers, we can calculate the number of skilled workers and clerks as follows:
Skilled workers = (8/5) * 20 = 32 Clerks = (1/5) * 20 = 4
Step 2: We also know that the ratio of the wages of a skilled worker, an unskilled worker, and a clerk is 5:2:3. Let's assume the common multiplier to be 'x'. So, the wages of the skilled worker, unskilled worker, and clerk would be 5x, 2x, and 3x respectively.
Step 3: The total daily wages for all employees is Rs. 3180. We can set up the following equation to find 'x':
(32 * 5x) + (20 * 2x) + (4 * 3x) = 3180 160x + 40x + 12x = 3180 212x = 3180 x = 3180 / 212 x = 15
Step 4: Now, we can find the daily wages paid to each category of employees:
Skilled workers = 5x = 5 * 15 = Rs. 75 Unskilled workers = 2x = 2 * 15 = Rs. 30 Clerks = 3x = 3 * 15 = Rs. 45
So, the daily wages paid to skilled workers, unskilled workers, and clerks are Rs. 75, Rs. 30, and Rs. 45 respectively.
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