Question

if 8 men took 10 hours to built a wall
how long it will take to built the same wall by 4 men???????​

Answer 1

$\underline{\bold{Given}}$

1st case :

Number of men = 8 (${x}_{1}$)

Time to built wall = 10 hours (${y}_{1}$)

2nd case :

Number of men = 4 (${x}_{2}$)

Time to built wall = ?? (${y}_{2}$)

As the number of men and time to built a wall is in inverse proportion.

$\underline{\bold{We\:know\:that,}}$

$\boxed{\bold{\dfrac{x_{1}}{x_{2}} = \dfrac{y_{2}}{y_{1}}}}$

$\bold{Let\:the\:time\:to\:built\:wall\:in\:second\:case\:be\:x.}$

According to the question,

$\implies\bold{\dfrac{8}{4} = \dfrac{x}{10}}$

$\implies\bold{\dfrac{8\times 10}{4} =x}$

$\implies\bold{20 = x}$

$\therefore$ if the number of men will be 4 then the time taken to built a wall will be 20 hours.

Answer 2

8 men takes 10hrs

so 1 man will take=8×10

=80hrs

4 men will take lesser time than 1 person doing the same work alone.hence time taken by them

=80/4

=20hrs