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A construction company ready to finish a construction work in $180$ days, hired $80$ workers each working $8$ hours daily. After $90$ days, only $2/7$ of the work was completed. How many workers are to be increased to complete the work on time?

Note: If additionally acquired workers do agree to work for $10$ hours daily.

  1. $90$ workers
  2. $80$ workers
  3. $65$ workers
  4. $85$ workers
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Case 1: When all the workers agree to work for 10 hours daily after 90 days.

Total time =180 days

Available workers = 80

Time per day = 8 hours

After 90 days i.e. 90 days are remaining

Completed work = 2/7

Remaining Work =5/7

So, we know that

(M1*D1*H1)/W1 = (M2*D2*H2)/W2

So, 80*90*8 / 2  =  M2*90*10 / 5

M2 = 160

So, We need 160-80 =80 more workers.

So, (B) is the correct answer.

 

Case 2: When only additionally hired workers to agree to work for 10 hours daily and the old workers remained working for 8 hours daily.

80 workers in 90 days complete = 2/7 work

80 workers in 180 days complete = 4/7 work

remaining work =1-4/7 = 3/7

So, we know that

(M1*D1*H1)/W1 = (M2*D2*H2)/W2

80*180*8 / 4  =  M2*90*10 / 3

 

M2 = 96

i.e. we need 96 more workers to complete work on time.

 

 

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$\rightarrow$ Suppose $1$ worker does $1$ unit of work in $1$ hour.

$\rightarrow$ So everyday a worker does $8$ units of work.

$\rightarrow$ Work done by $80$ such workers in $90$ days = ($90*80*8$) units = $57600$ units

$\rightarrow$ This $57600$ units of work is $\frac{2}{7}$th of the total work.

$\therefore$ Remaining work = $\frac{5}{7}$th of the total work = $57600 *\frac{7}{2}*\frac{5}{7}$ = $144000$ units

and Remaining days = $180-90$ = $90$ days


$\rightarrow$ Suppose ($80+x$) workers completes the remaining work in the remaining $90$ days

$\rightarrow$ Here $x$ extra workers and each one of them do $10$ units of work everyday for the remaining $90$ days.

$\rightarrow$The other $80$ workers, each of them do $8$ units of work everyday for the remaining $90$ days.

$\rightarrow$ Togather they have to complete $144000$ units of work in $90$ days

$\Rightarrow$ $(80*8*90) + (x*10*90) = 144000$

$\Rightarrow$ $(64*900) + (x*900) = 14400$

$\Rightarrow$ $64+ x=160$

$\Rightarrow$ $x=160-64 =96$

$\therefore$ We need $96$ extra workers to complete the remaining work in $90$ days.

Answer:

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