Question

• The average age of women and child workers in factory was 15 years.
The average age of all the 16 children was 8 years and the average
age of women workers was 22 years. If 10 women workers were
married, then the number of unmarried women workers is:

Answer 1

Answer:

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Step-by-step explanation:

Let the number of women workers be Y.

Then, 22y + 16 x 8 = 15 (16+y)

⇒ 22y + 128 = 240 + 15y

⇒ 22y - 15y= 240 - 128

∴ y = 16

∴ Unmarried women workers = 16 - 10 = 6

Answer 2

There are 6 unmarried women working in the factory.

There are 16 children and the average age of all the children is 8 years.

The sum of ages of all the children = $16\times 8 = 128$ years.

Let there be "x" number of women working in the factory.

The mean age of all the women is 22.

Therefore the sum of the ages of all the women = $22\times x =22x$

Total number of people (women and children) working in the factory = $16+x$

The average age of all the people in the factory is 15 years.

The sum of the ages of all the children and women in the factory = $15 \times(16+x) = 240+15x$

But we have calculated that the sum of all the people working in the factory is : $22x+128$

So we will form a linear equation in x to calculate the value of x.

$22x+128 =240+15x\\\\or, 22x-15x = 240-128\\\\or, 7x = 112\\\\or, x = 112\div7\\\\or, x=16$

There are 16 women workers in the factory. 10 of the women are married.

The number of unmarried workers = $16-10=6$

Therefore using a linear equation we calculate there are 6 unmarried women working in the factory.

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