Question

An average daily wages of $10$ workers in a factory '$A$' is Rs. $30$ and an average daily wages of $20$ workers in a factory '$B$' is Rs. $15$. Find the average daily wages of all workers of both the factories.

• A. $20$
• B. $40$
• C. $10$
• D. $15$

Answer 1

The correct option is A $20$

Average is the sum of the data values divided by the total number of data values.

i.e. $\text{Mean}=\frac{\text{Sum of the elements}}{\text{Total number of elements}}$.

Given that, average daily wages of $10$ workers in a factory $A$ is Rs. $30$.

$⟹30=\frac{\text{Sum of 10 workers daily wages}}{10}$

$⟹\text{Sum of 10 workers daily wages}=$ Rs. $300$.

Also, average daily wages of $20$ workers in a factory $B$ is Rs. $15$.

$⟹15=\frac{\text{Sum of 20 workers daily wages}}{20}$

$⟹\text{Sum of 20 workers daily wages}=300$.

Then, $\text{Total average}=\frac{\text{Sum of 10 workers daily wages + Sum of 20 workers daily wages}}{10+20}$

$=\frac{300+300}{30}=\frac{600}{30}=20$.

Therefore, the average daily wages of all workers of both the factories is Rs. $20$.

Hence, option $A$ is correct.