If 50 apprentices can finish a job in 4 hours, and 30

Question

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

Bunuel · Accepted Answer

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.

GMATinsight · Answer

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

TimeTraveller · Answer

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).

chetan2u · Answer

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

sasyaharry · Answer

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}

ScottTargetTestPrep · Answer

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

pavanbatra · Answer

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

Posted from my mobile device

KarishmaB · Answer

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.

bumpbot · Answer

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If 50 apprentices can finish a job in 4 hours, and 30

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