Ratio and proportion

[nidhis.1408]

3 machines have a productivity ratio of 1:2:5. all 3 machines are working on a job for 3 hours. at the beginning of the 4th hour, the slowest machine breaks. it is fixed at the beginning at hour 7, and begins working again. the job is done in 9 hours. what was the ratio of the work performed by the fastest machine to the work performed by the slowest?

[Anurag@Gurome]

3 machines have a productivity ratio of 1:2:5. all 3 machines are working on a job for 3 hours. at the beginning of the 4th hour, the slowest machine breaks. it is fixed at the beginning at hour 7, and begins working again. the job is done in 9 hours. what was the ratio of the work performed by the fastest machine to the work performed by the slowest?

Say the machines are A, B, and C.
Let us assume that in one hour A, B, and C can do x, 2x, and 5x fractions of the job.
Therefore, A is the slowest machine and C is the fastest.

Now, A has worked for 6 hours and C has worked for 9 hours.
Hence, in 6 hours A has done 6*x = 6x of the job and C has done 9*5x = 45x of the job

Hence, required ratio = 45x/6x = 15/2

[Shalabh's Quants]

3 machines have a productivity ratio of 1:2:5. all 3 machines are working on a job for 3 hours. at the beginning of the 4th hour, the slowest machine breaks. it is fixed at the beginning at hour 7, and begins working again. the job is done in 9 hours. what was the ratio of the work performed by the fastest machine to the work performed by the slowest?

In the first 3 hours, Slowest Machine will yield '1' amount of job, whereas fastest machine will yield '5' amount of job.

In 3rd 3 hour block(7th+8th+9th), Slowest Machine will yield another '1' amount of job, whereas fastest machine will yield another '5' amount of job.

In 2nd 3 hour block(4th+5th+6th), Slowest Machine will yield '0' amount of job, whereas fastest machine will yield another '5' amount of job.

Total amount of job in 9 hours by Slowest Machine will be equal to 1+1 = 2, & by fastest machine will be equal to 5+5+5 = 15.

=> Ratio of Output of Fastest machine to slowest machine will be equals to 15/2.

[karthikpandian19]

1:2:5 is the productivity ratio
slowest:medium:fastest

Find the hrs of working:
1:2:5 works for 3 hrs
then
2:5 works for 3hrs
then finally
1:2:5 work for 3hrs

So to sum it up: 1:2:5 works for 6 hrs & 2:5 works for 3 hrs

1 : 2 : 5
6 hrs : 2*9 hrs : 5*9 hrs

Fastest / Slowest required
45/18
Simply
5/2

3 machines have a productivity ratio of 1:2:5. all 3 machines are working on a job for 3 hours. at the beginning of the 4th hour, the slowest machine breaks. it is fixed at the beginning at hour 7, and begins working again. the job is done in 9 hours. what was the ratio of the work performed by the fastest machine to the work performed by the slowest?