If a group of 5 craftsmen takes 3 hours to finish a job

Question

If a group of 5 craftsmen takes 3 hours to finish a job, how long will it take a group of 4 apprentices to do the same job?

(1) An apprentice works at 2/3 the rate of a craftsman.

(2) The 5 craftsmen and the 4 apprentices working together will take 45/23 hours to finish the job

jedit · Answer

I figured D. 1- An apprentice works at 2/3 the rate of a craftsman. 5 craftsmen finish work in 3 hours. --> 1 craftsman does the job in = 5x3 = 15h --> 1 apprentice = 2/3 craftsman --> time by 1 apprentice will hence be reciprocal =15 x 3/2 = 45/2 = 22.5 --> time by 4 apprentices = 22.5/4 = 5.625 1 is -- clearly sufficient. 2- I kind of figured there is just one variable unknown which is the time taken by apprentices alone. We have rate of work of craftsmen and craftsmen + apprentices combined. One variable can be easily found. I actually found this question on a quick search, solved a few years ago. https://gmatclub.com/forum/work-word-pr ... ml#p843620

Kritisood · Answer

Bunuel has solved this one here  https://gmatclub.com/forum/work-word-problems-made-easy-87357.html

Bunuel · Answer

Time, rate and job in work problems are in the same relationship as time, speed (rate) and distance in rate problems.

time*speed=distance  <-->  time*rate=job \ done .

So, if we say that the rate of a craftsmen is  x  job/hours and the rate of an apprentice is  y  job/hour then we'll have  (5x)*3=job=(4y)*t  -->  (5x)*3=(4y)*t . Question:  t=\frac{15x}{4y}=?

(1) Each apprentice works at 2/3 the rate of a craftsman -->  y=\frac{2}{3}x  -->  \frac{x}{y}=\frac{3}{2}  -->  t=\frac{15x}{4y}=\frac{45}{8}  hours. Sufficient.

(2) The 5 craftsmen and the 4 apprentices working together will take 45/23 hours to finish the job --> as the 5 craftsmen need 3 hours to do the job then in 45/23 hours they'll complete (45/23)/3=15/23 rd of the job (15 parts out of 23) so the rest of the job, or 1-15/23=8/23 (8 parts out of 23) is done by the 4 apprentices in the same amount of time (45/23 hours):  \frac{5x}{4y}=\frac{15}{8}  -->  \frac{x}{y}=\frac{3}{2} , the same info as above. Sufficient.

Answer: D.

Louis14 · Answer

Could you please elaborate on the highlighted part?

yashikaaggarwal · Answer

we know 5 craftmen take 3 hours to complete 1 work.
we have to find out 5 craftmen will do how much work in 45/23 hours
5 crafts men is common in both statement.
so they do 1 work in 3 hours ( 1 work =3 hours)
and x work in 45/23 hours (x work = 45/23 hours)
cross multiplying,
x = (45/23)/3
x = 15/23
so 5 craftsmen can do 15/23 work in 45/23 hour.
hope its clear.

boat32674 · Answer

If a group of 5 craftsmen takes 3 hours to finish a job, how long will it take a group of 4 apprentices to do the same job?

(1) An apprentice works at 2/3 the rate of a craftsman.

But we don't know if both each apprentice works at same Rate and each craftsman work at same rate?? how can we assume this is true? maybe an apprentice work 2/3 rate and other 3 apprentice in group work at 1/3 rate

How can this be Sufficient

Bunuel · Answer

You are right — the question should have stated that each craftsman works at the same constant rate, and each apprentice works at the same constant rate.

If a group of 5 craftsmen takes 3 hours to finish a job

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If a group of 5 craftsmen takes 3 hours to finish a job

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