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

Question

The Book does not show any answers. Hence I need to figure out if I have done them correctly or not. Please help me if you can. Would greatly appropriate it. Thanks

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

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

Bunuel · Accepted Answer

The fastest worker who does 3 units of job worked for all 10 hours, so he did 3*10=30 units of job;

The slowest worker who does 1 unit of job worked for only 4+2=6 hours (first 4 hours and last 2 hours), so he did 1*6=6 units of job;

The ratio thus is 30 to 6, or 5 to 1.

Answer: C.

garc · Answer

I got to (C)

Ratio Setup 1:2:3, I ignored 2 as the question only asked for comparison between the slowest and fastest so it becomes 1:3. They each worked for (4) hours until the slowest took a break so the 4th hour ratio would look like

4th hour -4:12
5th hour - 4:15 (slowest worker takes a break until the 9th hour)
6th hour - 4:18
7th hour - 4:21
8th hour - 4:24
9th hour - 5:27
 10th hour - 6:30 = 1 to 5 ratio.

1 to 5 ratio slowest compared to fastest

flip it around as it is asking for a fastest to slowest comparison so it becomes 5 to 1.

geometric · Answer

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.

nhanlevent · 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.

bsahil · Answer

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

Bunuel · Answer

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.

PareshGmat · Answer

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

TGC · Answer

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!

havoc7860 · Answer

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

Bunuel · Answer

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.

Temurkhon · Answer

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

gracie · Answer

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

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

praneet87 · Answer

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

SeregaP · Answer

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

eddy8700 · Answer

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

vmelgargalan · Answer

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

SVaidyaraman · Answer

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.

Salsanousi · Answer

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

Posted from my mobile device

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

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