Respuesta :
Answer:
Number of days taken by 1 man alone and 1 boy alone are 35 days and 70 days respectively.
Step-by-step explanation:
Let, the work completed by 1 man in 1 day = x and the work completed by 1 boy in 1 day = y.
So, 4 men and 6 boy's 1 day work is [tex]\frac{4}{x}[/tex] and [tex]\frac{6}{y}[/tex]
And, 3 men and 4 boy's 1 day work is [tex]\frac{3}{x}[/tex] and [tex]\frac{4}{y}[/tex]
Since, 4 men and 6 boys complete the work in 5 days and 3 men and 4 boys complete the work in 7 days.
So, we have,
[tex]\frac{4}{x}+\frac{6}{y}=\frac{1}{5}[/tex]
[tex]\frac{3}{x}+\frac{4}{y}=\frac{1}{7}[/tex]
Let, [tex]u=\frac{1}{x}[/tex] and [tex]v=\frac{1}{y}[/tex]
So, the equations are,
[tex]4u+6v=\frac{1}{5}[/tex] ................(1)
[tex]3u+4v=\frac{1}{7}[/tex] ................(2)
Multiply (1) by 3 and (2) by 4 and subtract the equations, we get,
[tex]2v=\frac{1}{35}[/tex] i.e. [tex]v=\frac{1}{70}[/tex] i.e. [tex]\frac{1}{y}=\frac{1}{70}[/tex] i.e. y = 70.
Substitute value of 'v' in (1) gives,
[tex]4u+\frac{6}{70}=\frac{1}{5}[/tex] i.e. [tex]4u=\frac{-6}{70}+\frac{1}{5}[/tex] i.e. [tex]4u=\frac{8}{70}[/tex] i.e. [tex]u=\frac{8}{70\times 4}[/tex] i.e. [tex]u=\frac{1}{35}[/tex] i.e. [tex]\frac{1}{x}=\frac{1}{35}[/tex] i.e. x = 35
So, the number of days taken by 1 men alone and 1 boy alone are 35 days and 70 days respectively.
