Answer to Question #172949 in Algebra for amir

Question

Shiv want to lay a track 200 m long and 6 m wide using a team of 60 boys in 2 days. After 1 day, Shiv find 75 m x 6 m track has been laid. How many men should Shiv hire additionally if 2 men do the job of 5 boys?

Answer 1

60 boys can get the job done in 2 days.

So on the first day, 60 boys were able to lay 75m×6m. So, if these boys are allowed to do the work again, they would lay (75×2)m×6m = 150m ×6m.

But Shiv needs to lay 200m×6m. So what we have left is (200-150)m ×6m =50m×6m left to be accounted for.

Since 60 boys can do the job of 75m

Then 5boys will do $\dfrac{5×75}{60} = 6.25m$

But 2 men can do the job of 5boys, so we have that

2men can attend to 6.25 m length

$\dfrac{2×50}{6.25} = 16$ men can attend to 50m length.

So we have that Shiv needs to bring in 16 men to attend to the remaining 50m×6m left from what the 60boys can do in 2days.

And the perfect work plan is

Day 1 - 60 boys (75m×6m laid)

Day 2 - 60 boys (75m×6m laid) and 16 men (50m×6m laid).