Question

12 men 9 hours per day to complete the 40% of the work in 30 day. The rest work is done by 15 men, 6 hour per day. Then work done in how many days.

Answer 1

Step-by-step explanation:

We know this:

If men changed by n times, time is changed by (1/n) of the initial time.

Initial time 10*8 = 80 hours.

Final time 8*15 = 120 hours.

(1/n) of 80 = 120 implies n = (2/3)

The number of men required is (2/3) of 12 = 8

The work involves 12*8*10 = 960 man-hour-days for its completion.

So the number of men required to complete the same work in 8 days, working 15 hours a day = 960 man-hour-days/8*15 hour-days = 8 men.

Answer 2

Answer:

The rest of the work is completed in 54 days.

Step-by-step explanation:

Given the number of men working, $M_1= 12$

Number of days worked, $D_1= 30$

Number of working hours per day, $H_1= 9$

Completed work, $W_1= 40%$

Thus the remaining work,  $W_2=100-40=60\%$

To complete 60%, number of men working, $M_2= 15$

Number of working hours per day, $D_2= 6$

Let the number of days working, $D_2= x$

In the case of time and work, if $M_1$ men do $W_1$ work in $D_1$ days for $H_1$ hours per day and $M_2$ men do $W_2$ work in $D_2$ days for $H_2$ hours per day, then      

$\dfrac{M_1\times D_1\times H_1}{W_1} = \dfrac{M_2\times D_2\times H_2}{W_2}$

Substituting the given values,

$\dfrac{12\times 30\times 9}{40} = \dfrac{15\times x\times 6}{60}$

$\implies x=\dfrac{12\times 30\times 9\times 60}{40\times15\times 6} = 3\times 2\times 9=54$

Therefore, the rest of the work is completed in 54 days.

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