Proportion Problem!

Naturally, the amount of required time to assemble the car decreases as the number of workers increases. With 7 workers each working 8 hours, a total of 7 $\times$ 8 = 56 worker-hours are required to build one car.

Now with 12 workers, how many hours would each worker need to invest to assemble one car? Let $h$ be the number of hours each worker would have to contribute. We know that 56 worker-hours are required to build the car, so we can set up (and solve) the following equation:

$12h = 56 \longrightarrow h = \frac{14}{3}$

let capacity to work of each man be 'c' (as each man works at a constant rate) As 7 men work work 8 hours,so fraction of work completed by 7 men in 1 hour=

$\frac { 1 }{ 8 }$ th part of total work W i.e.

$\frac { 7 }{ c }= \frac { 1 }{ 8 } \times W$

from here $\frac { 1 }{ c } =\frac { 1 }{ 56 } \times W$

Now if there are 12 men with same capacity, then part of work completed in one hour= $12\times \frac { 1 }{ c } \times W$ = $12\times \frac { 1 }{ 56 } \times W$ = $\frac { 3 }{ 14 }\times W$

Therefore total time required in hours to complete whole work W = $\frac { 14 }{ 3 }$

when there are 7 workers each working 8 hours, there are a total of 56 hours worked.

since all the workers work at the same speed,with 12 workers you still need 56 hours worked all together.

                                                                     56 / 12 = 14 / 3

7× 8 ÷ 12 = 14 / 3

(8/12)×7=(2/3)×7=14/3 the easiest way to calculate

Since 7 workers complete the job in 8 hrs , 7 workers' 1 hrs work will b 1/8.

Similarly, 12 workers' 1 hour's work will b 1/8 x 12/7 = 3/14. (since,each worker works at the same, constant rate.)

Now, since 12 workers' 1 hrs work is 3/14 , they will require 14/3 hrs to complete the job . Because a whole job is considered to be unity i.e. 1

(8/12)×7=(2/3)×7=14/3

We can calculate the man hours needed and then we can divide it my no. of men to get no. of hours for particular no. of men. In this case total man hour is equal to 8*7=56 man-hours. So to find out time needed by 12 men we divide 56 by 12 which will come out to be 14/3 men.