Two machines A and B work at constant rates which are in the ratio of

Question

Two machines A and B work at constant rates which are in the ratio of 1:2 respectively. If the two machines work together, they can complete 1/3rd of a job in 3 hours. If machine A starts working on the job and works alone for 18 hours, how many hours would machine B working alone take to complete the remaining work?

A. 3.5
B. 4
C. 4.5
D. 5
E. 5.5

A. 3.5
B. 4
C. 4.5
D. 5
E. 5.5

yashikaaggarwal · Answer

A and B together can complete 1/3 job in 3 hours.
1 job in 9 hours.
Also, if A does x does 
B does 2x work
They together do 3x work in an hour
27x work in 9 hours.
A did work for 18 hours..
18*x = 18x work completed.
Remaining 27-18= 9x work
B can do 2x work in an hour.
9x/2x = 4.5 hour

Answer should be C

Posted from my mobile device

GMATinsight · Answer

Let, A makes 1 prdoct. in the time that B takes to make 2 products

i.e. Together in 1 hours they make = 1+2 = 3 Products

in 3 hours they make = 3*3 = 9

9 Products = (1/3) work (Given) 
 i.e. Work = 27 Products

Machine A in 18 hours will make = 18 products

Remaning products to make = 27-18 = 9

Time to B to complete 9 products = 9/2 = 4.5 hours

Answer: Option C

satya2029 · Answer

A and B are rates of machines A and B respectively, and they are in 1:2
(Ra+2Ra)*3=1/3
Ra=1/27
in 18 hrs work done by A= 2/3 of the work
remaining work=1/3
for B
2Ra*t=1/3
t=1/6Ra
t=27/6
t=4.5 
C:)

Archit3110 · Answer

rate of A= 1 and rate of B =2
so in 3 hours work done ; (1+2)*3 = x/3
total work = 27
if A works 18 hours ; left with 27-18; 9 units
which B will do in 9/2 ; 4.5 hours
OPTION C

Starscreen60 · Answer

I tried to solve this question my own way and really couldn't get the answer, can someone help?

If worker B's rate is 1/x, the slower workers rate will be 1/2x. Now, we know it takes them 3 hours to complete 1/3rd of the task, so 9 hours for the full task.  1/x + 1/2x = 1/9

Based on this, I can solve for the rate of the 2 workers, and get B as 2/27 and A as 2/54.

If A works for 18 hours, it does (2/54)*18 amount of work, which is 2/3rd of the work. Remaining work is (2/3)*(1/9). This is where I'm getting 2/27, so it would take machine B 1 hour to do the remaining work.

Where am I going wrong? Thanks. cc  Bunuel

Flower_Child · Answer

You did the mistake in the last line -
 "If A works for 18 hours, it does (2/54)*18 amount of work, which is 2/3rd of the work. Remaining work is (2/3)*(1/9). This is where I'm getting 2/27, so it would take machine B 1 hour to do the remaining work."

A completed 2/3rd of the work. Correct
Work remaining for B = 1/3rd. Rate of B = 2/27
So time =  \frac{Work }{ Rate }=\frac{1}{3} * \frac{27}{2 } = \frac{9}{2} = 4.5

Two machines A and B work at constant rates which are in the ratio of

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Two machines A and B work at constant rates which are in the ratio of

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards