Proportion questions related fourth proportions I have a couple of basic Proportion questions that I am unable to solve.


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*18 men build a wall that is 140m long in 42 days.  How long would it take 30 men to build a wall that is 100m long?

*In a factory, the ratio of male workers to female workers is 5:3. If there are 40 less female workers than male workers, what is the total number of workers in the factory?

1. Solution to Problem 1
Let's say each person does $x$ amount of work each day. Work done by $18$ men in $42$ days will be equal to constructing $140$ m wall. $$18\times42\times x=140$$
$$\Rightarrow x=\frac{140}{18\times42}$$
and if time taken by $30$ men to build $100$m wall is $y$ then
$$30\times y \times x=100$$
$$\Rightarrow y=\frac{100\times42\times18}{30\times140}=18\text{ days}$$
2. Solution to Problem 2
Let there be $x$ males and $y$ females
Then we have
$$5y=3x$$
$$x-y=40$$
Solving these two equations we get
$$x=100 , y=60$$
