Each of 10 machines works at the same constant rate doing a

Question

Each of 10 machines works at the same constant rate doing a certain job. The amount of time needed by the 10 machines, working together, to complete the job is 16 hours. How many hours would be needed if only 8 machines, working together, were used to complete the job?

A. 18
B. 20
C. 22
D. 24
E. 26

A. 18
B. 20
C. 22
D. 24
E. 26

In the test I ticked the answer as 20, which was correct but it was random guess. Can someone explain how to solve these questions? What to equate? what to look for? etc.etc. i.e what is the main logic behind to solve these problems.

Bunuel · Accepted Answer

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

Time*Rate=Distance
Time*Rate=Job

Given:  16*10x=job . Question: if  t*8x=job  (the same job), then  t=?

Solving for  t :  16*10x=t*8x  -->  t=20 .

Answer: B.

Hope it helps.

raghavs · Answer

go by this split:

10 Machines--16Hrs--1work
1 Machines--160Hrs--1work
8 Machines--20Hrs--1work

gsaxena26 · Answer

So correct me if I am wrong:

x -> Rate of 1 machine and therefore rate of 10 machines is 10x.

I understand the rest of it. Thanks.

Bunuel · Answer

Yes, that is correct. Below are some work problems with explanations: ps-explanation-92679.html#p713495 facing-problem-with-this-question-91187.html?highlight=rate+reciprocal what-am-i-doing-wrong-to-bunuel-91124.html?highlight=rate+reciprocal Hope it helps.

GMATBLACKBELT720 · Answer

1job/16hrs for 10 machines. Thus (1/16)/10 -> 1/160hrs for 1 machine. -> 1/160*8 = 1/20 -> 20 hrs.

mustdoit · Answer

I would do this question as under:

Let total work be 160 pages

At present 
10 machines take 16 hours each to type 160 pages
That gives one machine types 16 pages in 16 hrs or 1 page per hour

Required
8 machines and 160 pages

Obviously given the speed of 1 page per hour the total time required would be 20hrs.

Hope this helps....

ykaiim · Answer

time1 x speed1 = time2 x speed2

So, OA is B.

dimitri92 · Answer

i usually convert such questions into machine-hours

10 machines in 16 hours =  10*16  machine-hours

8 machines will take =  \frac{10*16}{8} = 20  hours

Answer: B

HTH

abid1986 · Answer

This is a case of direct inverse variation

Number of Machine varies inversely with time
i.e as number of machines will increase ,time taken to complete job would become less .

10 Machine .........16 hrs
8 machine.......... x hrs?
x = 16 *(10/8)
x = 20 hrs

adityapagadala · Answer

The general formula is

MDH/w = constant i.e M1D1H1/W1 = M2D2H2/W2 where M = man/machines D = days H = hours in days and W = work

Here D & W are constant so M1H1 = M2H2 => 10*16 = 8* x => x= 20

dheeraj24 · Answer

1/16th of the work is completed in 1hr by 10 machines .
???? of the work is completed in 1 hr by 1 machine ----> 1/160th of the work is completed by 1 machine in 1 hr.

8 machines in 1 hr complete ---> 8 *1/160 = 1/20th of the work.
20 hrs needed for whole machines.

Salvetor · Answer

Rate 
10 Machine = 1/16
1 Machine = 1/160
8 Machine = 1/20

Rate x Time = Work 
1/20 x T= 1
so T = 20

BrentGMATPrepNow · Answer

The amount of the time needed by the 10 machines working together, to complete the job is 16 hours.  
So, we can say that the job requires a total of  160 MACHINE HOURS  (10 machines each working 16 hours = 160 machine hours)

How many hours would be needed if only 8 of the machines, working together, were used to complete the job?  
We need to divide the work of  160 machine hours  among the  8  machines. 
 160 / 8  = 20 hours

Answer:  B

Abhishek009 · Answer

Let total work be 160 units

So, Efficiency of each machine is 1 unit...

Time required by 8 machines, working together will be 160/8 = 20 hours..
  
Hence answer will be (B) 20

sasyaharry · Answer

Since work done is the same, we can equate the two equations 
Rate of 10 machines is 10*R, time is 16hrs
Rate of 8 machines is 8*R, time is t hrs

8R*t = 10R*16
t=20

Answer is  B

hasnain3047 · Answer

rate of 10 machines  = \frac{1}{16} 
rate of 1 machine  = \frac{1}{160} 
rate of 8 machines  = 8/160 = \frac{1}{20} 
so 8 machines would require 20 hours to complete job.

sumit411 · Answer

20 hours. Check out the solution Kudos appreciated IMG_20180820_232858.jpg Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app

Pritishd · Answer

Machines (M), Work (W) and Time (T)

M T W
10 16 1
1 16 1/10
1 1 1/160
8 1 1/20
8 20 1

Ans: 20 Hours

Kimberly77 · Answer

Hi  BrentGMATPrepNow . It seems using ratio for this question do not arrive at correct answer?

10 Machine = 16 hrs
8 machine = x 
x = (16 * 8)/10
x = 128/10 = 12.8 hrs

Each of 10 machines works at the same constant rate doing a

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