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cv3t3l1na
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If 50 apprentices can finish a job in 4 hours, and 30   Updated on: 18 Jul 2013, 11:32
Originally posted by cv3t3l1na on 23 Nov 2012, 06:21.
Last edited by Bunuel on 18 Jul 2013, 11:32, edited 2 times in total.
Renamed the topic, edited the question and the OA.
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If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 4,5 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour?

A. 1/9
B. 29/180
C. 26/143
D. 1/5
E. 39/121
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B
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If 50 apprentices can finish a job in 4 hours, and 30   23 Nov 2012, 06:36
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cv3t3l1na
If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 4,5 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour?

A. 1/9
B. 29/180
C. 26/143
D. 1/5
E. 39/121
50 apprentices can finish the job in 4 hours, thus:
10 apprentices can finish the job in 4*5 = 20 hours;
In 1 hour 10 apprentices can finish 1/20 of the job.

30 journeymen can finish the same job in 4,5 hours, thus:
15 journeymen can finish the job in 4.5*2 = 9 hours;
In 1 hour 15 journeymen can finish 1/9 of the job.

Therefore, in 1 hour 10 apprentices and 15 journeymen can finish 1/20+1/9=29/180 of the job.

Answer: B.
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If 50 apprentices can finish a job in 4 hours, and 30   21 Jul 2015, 22:48
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cv3t3l1na
If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 4,5 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour?

A. 1/9
B. 29/180
C. 26/143
D. 1/5
E. 39/121

CONCEPT: \(\frac{(Machine_Power * Time)}{Work} = Constant\)

i.e. \(\frac{(M_1 * T_1)}{W_1} = \frac{(M_2 * T_2)}{W_2}\)

Let, Work = W
Apprentice = A
Journeyman = J

i.e. \(\frac{(50A * 4)}{W} = \frac{(30J * 4.5)}{W}\)

i.e. 20A = 13.5J

i.e. 10 apprentices and 15 journeymen = 10A + 15J = 13.5J/2 + 15J = 21.75J

Now, \(\frac{(21.75J * 1)}{W_1} = \frac{(30J * 4.5)}{W}\)

i.e. \(W_1 = 21.75J*W/30*4.5J = 29*W/180\)

Answer: option B
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If 50 apprentices can finish a job in 4 hours, and 30   21 Jul 2015, 23:35
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Apprentices: 50 * 4 = 200 job-hours. 1 apprentice's job-hour = 1/200.

Journeymen: 30 * 4.5 = 135 job-hours. 1 journeymen's job-hour = 1/135.

Job done by (10 apprentices + 15 journeymen) = 10/200 + 15/135 = 1/20 + 1/9 = 29/180. Ans (B).
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If 50 apprentices can finish a job in 4 hours, and 30   16 Oct 2017, 12:11
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If 50 apprentices can finish a job in 4 hours and 30 skilled workers can finish the same job in 9/2 hours, how much of the job should be completed by 10 apprentices and 15 skilled workers in 1 hour?

(A) 1/9
(B) 29/180
(C) 26/143
(D) 1/5
(E) 39/121


hi..

If 50 apprentices can finish a job in 4 hours, 10 apprentices will finish it in \(4*\frac{50}{10}=20\)
so 1 hour work of 10 apprentices = \(\frac{1}{20}\)

and 30 skilled workers can finish the same job in 9/2 hours, so 15 will do it in 9 h
so 1 hour work of 15 skilled workers = \(\frac{1}{9}\)

so their combined work = \(\frac{1}{20}+\frac{1}{9}=\frac{29}{180}\)

B
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If 50 apprentices can finish a job in 4 hours, and 30   19 Oct 2017, 17:58
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First, find individual rates.

Apprentices:

50 complete 1 job in 4 hours.
50 complete 1/4th of a job in 1 hour.
1 completes\(\frac{1}{4*50}\) or\(\frac{1}{200}\) of a job in 1 hour.

Similarly for skilled workers:

30 complete 1 job in 9/2 hours.
30 complete 2/9 of the job in 1 hour.
1 completes \(\frac{2}{9*30}\) or \(\frac{2}{270}\) or \(\frac{1}{135}\) job in 1 hour.

Work done by 10 Apprentices and 15 skilled workers in 1 hour = \(10*\frac{1}{200}+15*\frac{1}{135} = \frac{29}{180}\)
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If 50 apprentices can finish a job in 4 hours, and 30   24 Oct 2017, 06:45
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Bunuel
If 50 apprentices can finish a job in 4 hours and 30 skilled workers can finish the same job in 9/2 hours, how much of the job should be completed by 10 apprentices and 15 skilled workers in 1 hour?

(A) 1/9
(B) 29/180
(C) 26/143
(D) 1/5
(E) 39/121

The rate of 50 apprentices is 1/4 and the rate of 30 skilled workers is 1/(9/2) = 2/9.

We can use a proportion to determine n, the rate of 10 apprentices:

50/(1/4) = 10/n

200 = 10/n

200n = 10

n = 10/200 = 1/20

We can also use a proportion to determine m, the rate of 15 skilled workers:

30/(2/9) = 15/m

(9 x 30)/2 = 15/m

135 = 15/m

135m = 15

m = 15/135 = 1/9

Thus, the fraction of a job completed by 10 apprentices and 15 skilled workers in 1 hour is 1/20 + 1/9 = 9/180 + 20/180 = 29/180.

Answer: B
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If 50 apprentices can finish a job in 4 hours, and 30   25 Mar 2021, 14:36
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can anyone please explain what's wrong here?

50 apprentices take 4 hours.. so each hour they would complete 50/4 =25/2 of the job.

each apprentice would do 1/50 × 25/2 = 1/4 of the job.

but the actual rate of each apprentice is 1/20.

i'm unable to grasp my mistake. Bunuel VeritasKarishma please help

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If 50 apprentices can finish a job in 4 hours, and 30   26 Mar 2021, 02:31
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pavanbatra
can anyone please explain what's wrong here?

50 apprentices take 4 hours.. so each hour they would complete 50/4 =25/2 of the job.

each apprentice would do 1/50 × 25/2 = 1/4 of the job.

but the actual rate of each apprentice is 1/20.

i'm unable to grasp my mistake. Bunuel VeritasKarishma please help

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50 apprentices take 4 hours.. so each hour they would complete 50/4 =25/2 of the job.

This is not correct. They need to complete 1 job. They complete it in 4 hrs. It means, every hour 50 apprentices work together to complete 1/4th of the job.

50 apprentices complete 1/4th of the job every hour
So 10 apprentices must be doing (1/4)/5 = 1/20th of the job every hour

Note what is meant by 25/2 of the job. This is equal to 12.5 of the job i.e. 12.5 times the initial job.
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