Problem Solving

It takes 12 days for 6 machines working together at their respective rates to complete a job. How many more machines will be needed to reduce the number of days from 12 to 8 days?

Machine hours = 6*12 = 72.

Now if work has to be done in 8 days, x*8=72
x=9.

Therefore 3 more machines are needed

(12*6)/1 = (6+n)*8/1 . The 1 represents the work done

n=3

rnaah wrote:It takes 12 days for 6 machines working together at their respective rates to complete a job. How many more machines will be needed to reduce the number of days from 12 to 8 days?

We know

Work = Time taken * No of workers



here it is given It takes 12 days for 6 machines to complete a job.


so the total work can be found out as 12 * 6 = 72 units



Now we have found out the total work and we are required to find out the No of workers when timme taken reduces to 8 units...


again we go thru the same formula :

Work = Time taken * No of workers


72 = 8 * No of workers


So , 9 = No of workers

Just Different way of doing It, once if you understand this logic behind a kind of problem then it would be very easy for you. Try this

6 Machines in 12 Days completes 1 piece of work
1 Machine in 12 Days completes 1/6 of work
1 Machine in 1 Day completes 1/6*12 = 1/72 of work

Which means
Machines * Days * rate (Rate per day per machine) = 1

So, let us say number of new Machines = x
then, x * 8 * 1/72 = 1
x*8 = 72
x = 9

Answer = 9 - 6 = 3

Thanks,
SVD