A can complete the job in 2 hours and B can complete the sam

Question

A can complete the job in 2 hours and B can complete the same job in 3 hours. A works for 1 hour and then B joins and both complete the job. What fraction of the job did B complete

A. 1/5
B. 3/10
C. 1/2
D. 5/6
E. 8/9

KanishkM · Accepted Answer

Total work = 6 units

In 1 hr, A does = 3 units/hr 
In 1 hr, B does = 2 units/hr

Now If A starts the work he completes 3 units of work already

Now they both can complete the 3 units work in => 5 units/hr ====> 3 units

3/5 hours

Now B would have worked for = 2 *3/5 = 6/5

which is what fraction of 6 units => 6/5 = x 6

x = 1/5

A

fluke · Answer

A's rate = 1/2 W/h
B's rate = 1/3 W/h

In 1 hour A finished 1/2 W.

Only half of the work is left to be completed.

Together A and B can finish 1 work in;
1/2+1/3=1/t
t = 6/5 hours

So; they would have finished (1/2)W in half the time;

6/5*1/2 = 6/10 =(3/5)hour

B does 1/3 W in 1 hour
So, in 3/5 hour => 3/5*1/3 = 1/5 Work

Ans: "A"

subhashghosh · Answer

1/2 + 1/3 = 5/6

so together they complete in 6/5 hrs and in 3/5 hrs they do 1/2 of Job together.

1/2 of job is done by A already, so they do remaning 1/2 and take 3/5 hrs for it.

So if B does 1/3 of job in 1 hr

in 3/5 hrs he'll complete 3/5 * 1/3 = 1/5 of Job

Answer - A

jlgdr · Answer

A does have of the job alone so 1/2 remains. Both A and B together do 5/6 of a job in an hour hence to do 1/2 of the job they will take 3/5 of an hour. In this time B does 3/5*1/3 = 1/5 of the job

Hence A is the correct answer choice

Please let me know if anything remains unclear
Cheers
J

PareshGmat · Answer

................................ Rate .............. Time ................. Work

A ................................  \frac{1}{2}  ............... 2 ....................... 1

B ..............................  \frac{1}{3}  .................. 3 ........................ 1

Work done by A alone in 1 hour  = \frac{1}{2} * 1 = \frac{1}{2}

Pending work  = 1 - \frac{1}{2} = \frac{1}{2}

Combined rate of A & B = \frac{1}{2} + \frac{1}{3} = \frac{5}{6}

Time required for A & B combine to complete the remaining work  = \frac{\frac{1}{2}}{\frac{5}{6}} = \frac{3}{5}

Work done by B in the combined effort  = \frac{1}{3} * \frac{3}{5} = \frac{1}{5}

Answer = A

EMPOWERgmatRichC · Answer

Hi All,

The answer choices to this question are really helpful in getting to the correct answer - they're "spread out" enough that we can avoid almost all of the math and solve this with some logic and a "comparison."

We're told that A can complete a job in 2 hours and B can complete a job in 3 hours.

Next, we're told that A works alone for 1 hour. This means that A complete 1/2 of the job before B even shows up, so only 1/2 of the job remains to be completed.

If A and B worked at the SAME rate, then each would do "half of the half" of the job that's left. In total, A would end up doing 3/4 and B would end up doing 1/4 of the job.

HOWEVER, A works FASTER than B (2 hrs to 3 hrs to complete the job, respectively), so A does MORE than "half of the half" of the job that's left. This means that A does MORE then 3/4 and B does LESS than 1/4. Looking at the answers, there's only one that is LESS THAN 1/4.

Final Answer:  A

GMAT assassins aren't born, they're made,
Rich

gracie · Answer

t=time for A and B to complete job
t/2+t/3=1/2 of job
t=3/5 hour
(3/5)(1/3)=3/15=1/5 of job done by B

bumpbot · Answer

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A can complete the job in 2 hours and B can complete the sam

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