Question

The ratio of the male and the female worker in the factory is 8 : 5. If there are 104 male workers, find the number of female workers.

Answer 1

Hint: The ratio of the quantity gives the idea of how many times one quantity is greater or smaller than the other quantity. The ratio is always a pure number; it doesn’t have any unit since it is a quotient of two quantities with the same unit.

Complete step-by-step answer:
Suppose the number of male in the factory be \[8x\] and the number of females be \[5x\].
Since the number of male workers in the factory is 104.
Therefore,
\[8x=104\]
Solve the above equation and find the value of \[x\]:
  $ 8x=104 $
 $ x=\dfrac{104}{8}\text{ (Divide both sides by 8)} $
 $ x=13 $
Thus, the value of \[x\] is 13.
Now, calculate the number of females in the factory.
Since, the number of females in the factory is \[5x\].
Therefore,
  $ 5x=5\left( 13 \right)\text{ (Since, }x=13\text{)} $
 $ 5x=65 $
Hence,
The number of females in the factory is 65.

Note: The given question can be solved in an alternative way. This is discussed below:
Suppose the total number of workers in the factory be \[x\].
Since, the ratio of male to female workers in the factory is 8:5.
Therefore,
The numbers of male workers are given by \[\dfrac{8}{8+5}\times x=\dfrac{8}{13}\times x\]
Since, the number male workers is 104. Therefore,
  $ \dfrac{8}{8+5}\times x=104 $
 $ \dfrac{8}{13}\times x=104 $
 $ x=\dfrac{104\times 13}{8} $
 $ x=169 $

  $ \text{Number of female workers}+\text{Number of male workers}=\text{Total number of workers} $
 $ \text{Number of female workers}=\text{Total number of workers}-\text{Number of male workers} $
 $ \text{Number of female workers}=\text{169}-104 $
 $ \text{Number of female workers}=65 $
Thus,
The numbers of female workers are 65 in the factory.
Also, always take the sum of the ratio at the denominator and anyone corresponding ratio at the numerator while solving for the particular ratio.