Question

40 men planned to complete a certain work in 20

days working 6 hours per days. After 15 days only

3/5 th of the work was completed, how many extra

men required to complete the work on time working

8 hours per day ?​

Answer 1

Given :

40 men planned to complete a certain work in 20  days working 6 hours per days.

After 15 days only  $\dfrac{3}{5}$of the work was completed

To Find :

The number of extra  men required to complete the work on time working  8 hours per day

Solution :

Let The number of extra men = x

We know,

$\dfrac{men\times days\times hours}{work}$  = constant

The number of men = $m_1$ = 40

The number of days = $d_1$ = 15

The number of hours = $h_1$ = 6  per days

Work done = $w_1$ = $\dfrac{3}{5}$

Again

The number of men = $m_2$ = ( 40 + x )

The number of days = $d_2$ = 5

The number of hours = $h_2$ = 8  per days

Work done = $w_2$ = 1 - $\dfrac{3}{5}$ = $\dfrac{2}{5}$

So,   $\dfrac{m_1\times d_1\times h_1}{w_1}$  =  $\dfrac{m_2\times d_2\times h_2}{w_2}$

Or,  $\dfrac{40\times 15\times 6}{\dfrac{3}{5} }$  =    $\dfrac{(40+x)\times 5\times 8}{\dfrac{2}{5} }$  

or,   $\dfrac{40\times 15\times 6}{3}$ =   $\dfrac{(40+x)\times 5\times 8}{2 }$

Or,   40 × 5 × 6  = ( 40 + x ) × 5 × 4  

Or,  1200 = 800 + 20 x

Or,  20 x = 1200 - 800

Or,  20 x = 400

∴           x = $\dfrac{400}{20}$

i.e         x = 20

So, number of extra men = 20

Hence, The  number of extra  men required to complete the work on time working  8 hours per day is 20 . Answer