Question

25 men with 10 boys can do in 6 days as much work as 21 men with 30 boys can do in 5 days. How many boys must help 40 men to do the same work in 4 days ?

Answer 1

Hint: Assume the work done by each man and boy in one day, the assumed quantity multiplied with the number of man and boy respectively will give the amount of work done in 1 day, multiply this equation with the number of days to find the complete work done. Compare the equations with each other to find out the required quantity.

Complete step-by-step answer:
25 men and 10 boys together complete a work in 6 days.
Let the work done by each man be x and the work done by each boy be y, so the above statement can be written in terms of x and y as follows –
 $ 6(25x + 10y) = 1 $
The same amount of work is completed by 21 men and 30 boys in 5 days, this statement can be written as –
 $ 5(21x + 30y) = 1 $
As the work done is the same in both cases, we can compare them as follows –
 $ 6(25x + 10y) = 5(21x + 30y) $
0n solving the equation further, we get –
 $
\Rightarrow 150x + 60y = 105x + 150y \\
\Rightarrow 45x = 90y \\
\Rightarrow x = 2y \;
  $
Now, we have to find the number of boys required to help 40 men in completing the same work in 4 days, let the number of boys be a.
This statement can be written in equation form as, $ 4(40x + ay) = 1 $
As the work done in this case is the same as the work done in the above two cases, so we can equate it with any of the two equations.
 $
\Rightarrow 4(40x + ay) = 6(25x + 10y) \\
\Rightarrow 160x + 4ay = 150x + 60y \\
\Rightarrow 4ay = 60y - 10x \\
\Rightarrow 4ay = 60y - 10(2y) \\
\Rightarrow 4ay = 40y \\
   \Rightarrow a = 10 \;
  $
Hence, 10 boys should help 40 men for completing the work in 4 days.
So, the correct answer is “10”.

Note: As we are given two different kinds of people who are doing the work, so we have to assume two constant quantities to convert the given statements into equations. Converting them into equations is necessary so that they can be solved easily. We assume the amount of work done by one man and one boy, the work done by a given number of men or boys is equal to the assumed quantity multiplied with that number.