Three workers have a productivity ratio of 1 to 2 to 3. All

This is a nice problem because it offers the chance to quite easily intuitively solve a problem. Maybe @Bunuel can go into detail how to systematically solve this problem and problems like it (i.e., problems like it that are much harder)? Here's how to use intuition though:

Ratio is 1:2:3 for slow:medium:fast.

Medium and fast each work for 10 hours, while slow works for 6 hours because he skipped 4 hours.

So in 10 hours, fast does 30 units if work, and in 10 hours, medium does 20 units of work, while in 6 hours, slow does 6 units of work.

So, the job required 56 units of work, 30 of which were done by fast and 6 of which were done by slow. so 30 to 6 = 5 to 1.

Therefore, C is the answer.

Let A, B, C be the rates of the slowest to the fastest workers, respectively. --> C = 3A

A worked for 6 hours since he skipped 4 hours from the 5th to the 8th while C worked for 10 hours. --> Total work of A = 6A and total work of C = 10C

Work C/Work A = 10C/6A= (10*3A)/6A = 5/1 --> C.

Hello,


Could anyone just help me interpret "productivity ratio of 1 to 2 to 3"

I could come to conclusion that for first worker rate is 3 units of work per hour.

Also what would the rate for other two(B & C) workers

Anybody please explain

Three workers have a productivity ratio of 1 to 2 to 3, means that if A does 1 unit of work in an hour, then B does 2 and C does 3. A's rate in this case is 1 unit/hour, B's 1/2 unit/hour and C's 1/3 unit/hour.

Productivity ratio 1:2:3 (for ex: A:B:C) is B is twice as much productive as A & C is thrice as much productive as A

So, between A, B & C, A is least productive & C is most productive.

As far as B:C is concerned, it will still be 2:3

Another Approach:

More the productivity More the rate. Hence,

1:2:3

Consider X,2x, and 3x where person having rate x is slowest and person having rate 3x is fastest.

All of them work for 6 hours in total 10 hours. Then,

x+2x+3x = 6x Rate

Rate * Time = Work
6x * 6 = 36x

And 3x+2x=5x (Both of the other two work for extra 4 hours in 10 hours)

5x * 4 = 20x

Total work = 20x + 36x = 56x

Fastest worker does work for 10 hours hence Work(Fast) = 30x
Slowest worker does work for 6 hours hence Work(Slow) = 6x

Ratio = 30/6 = 5/1

Rgds,
TGC!

Hi Bunuel you say that the slowest worker worked for 4+2=6 hours( first 4 hours and last 2 hours) should it not be 5+1=6 since the question says that the slowest worker takes a break at the beginning of the fifth hour which means he has worked for 5 hours and also he joins back at the beginning of the 9th hour and the work completes in 10 hours which means after joining he worked only for an hour? please correct me if i am wrong

No.

At the beginning of the 5th hour, the slowest worker takes a break, means that this worker worked only for the first 4 hours (he left when 5th hour started).

The slowest worker comes back to work at the beginning of the 9th hour and begins working again, means that this worker worked for 9th hour.

R*T = W

Slow - 1/3w/h
Fast - 1w/h

1/3*4+1/3*2=4/3+2/3=6/3=2

1*4+1*4+1*2=10

10:2=5:1

C

Three workers have a productivity ratio of 1 to 2 to 3. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 9th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?

A. 12 to 1
B. 6 to 1
C. 5 to 1
D. 1 to 6
E. 1 to 5

if all 3 work all 10 hours,
then work ratio of fastest to slowest is 10*3/10*1=3/1
but slowest worked only 6 hours, so ratio is 10*3/6*1=5/1
C

Beginning of the 9th hour. The word beginning is the key.

Let's ignore the middle worker:
Productivity ratio: 1:3
1-4 hours slowest did 4 quickest did 3*4
10 hours: slowest did 4+2, quickest did 3*10
Hence the work ratio is 6:30
the fastest to slowest is 30:6 or 5:1, hence, C

The fastest worker worked for entire 10 hours i.e he must have completed 30 units in 10 hrs

The slowest worker who worked for 6 hours must have completed 6 units
hence 30/6 5 to 1
answer C

Hey Bunnel, I actually solved it right except I made a quite a silly mistake. When it says the job takes 10 hours to do, does it include the 10th hour? so would it be 9 full hours or 10 full hours for the work done? this was confusing so i had 30\7

1. (time worked by slowest worker)/ (time taken by slowest worker working alone) +(time worked by fastest worker)/ (time taken by fastest worker workign alone)+(time worked by third worker)/ (time taken by third worker working alone)
2. (4+2)/3x + 10/x + 10/2x=1
3. Ratio of work performed by fastest to slowest is (10/x)/(6/3x)=5 to 1

Note: Time taken when working alone is given by the productivity.

Since they are in ratios

1x:2x:3x

Let x = 1/6

This way the rates will be 1/6, 1/3 and 1/2 respectively.

The fastest worker did 10 hours of work that is 10 * (1/2) = 5

the slowest worker did 4 hours first then came back to finish the 9th hour and the 10th

total hours worked = 6 for slowest

6 * 1/6 = 1

ratio is then 5:1

Answer choice C

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