When working independently, machine A can complete a piece of work in

Question

When working independently, machine A can complete a piece of work in 10 hours, and machine B can complete the same wok in 6 hours. Both machines worked together for 3 hours, and then Machine A stopped working. How much more time did machine B take to complete the remaining work ?

A.

B.

C.

D.

E.

A.  1 hour
 B.  1 hours 12 minutes
 C.  1 hour 20 minutes
 D.  1 hour 48 minutes
 E.  2 hours

To read all our articles:  Must Read Articles and Practice Questions to score Q51

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Ability-Quiz-WP-e1533292133520.png

Archit3110 · Answer

ra = 1/10 ; rb= 1/6
combined rate = 16/60 ; 4/15

combined work done in 3 hrs = 4 * 3 /15 = 4x/5 
left x/5
so time taken by B 
x/5 * 6= time
x=1
1.2 hrs or say 1.2* 60= 72 mins ~ 1 hr 12 mins IMO B

eswarchethu135 · Answer

work done by A in 1 hour =  \frac{1}{10}

work done by B in 1 hour =  \frac{1}{6}

work done by A and B in 1 hour =  \frac{1}{10}  +  \frac{1}{6}

=  \frac{16}{60}

They worked together for 3 hours. So  3*\frac{16}{60}

\frac{16}{20}

Remaining work is  \frac{4}{20}

Now A stopped working and B has to complete the work.

x*\frac{1}{6}  =  \frac{4}{20}

x =  \frac{24}{20}

x =  \frac{24}{20}*60  minutes

x = 72 minutes or 1 hour 12 minutes.

OPTION:  B

kenjiko · Answer

LCM is 60, so it is equivalent to say that:
 A produces 6 units every hour
 B produces 10 units every hour

So in 3 hours we have 3(6+10) = 48 units of 60
So B needs to produce 12 remaining units in x hours

10 units in 1 hour
12 units in x hour
x = 1,2 hour or 1hour and 12 min

EgmatQuantExpert · Answer

Solution

Given:  
In this question, we are given
 • Working independently, machine A can complete a piece of work in 10 hours.
• Working independently, machine B can complete a piece of work in 6 hours.
• Both machines worked together for 3 hours, and then machine A stopped working.
• The remaining work was completed by machine B, working alone.

To find:  
We need to determine
 • The extra time taken by machine B, to complete the remaining work.

Approach and Working:  
Let us assume the total work to be the LCM (10, 6, 3) = 30 units

In 10 hours, machine A does 30 units of work.
 • Hence, in 1 hour, machine A does  \frac{30}{10}  = 3 units of work

In 6 hours, machine B does 30 units of work.
 • Hence, in 1 hour, machine B does  \frac{30}{6}  = 5 units of work

In 1 hour, machine A and machine B together can finish (3 + 5) = 8 units

As they worked for 3 hours together, total work completed in those 3 hours = (8 x 3) units = 24 units.
 • Remaining work after 3 hours = (30 – 24) units = 6 units

As machine B completed the remaining work alone, the extra time taken beyond 3 hours =  \frac{6}{5}  hours = 1 hour 12 minutes.

Hence the correct answer is Option B.

Answer: B

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Ability-Quiz-WP-e1533292133520.png

ScottTargetTestPrep · Answer

Machine A’s rate is 1/10, and machine A worked for 3 hours. Machine B’s rate is 1/6. If we let n = the extra time that machine B worked, then machine B worked for (3 + n) hours. We can create the equation:

(1/10)(3) + (1/6)(3 + n) = 1

3/10 + (3+n)/6 = 1

Multiplying by 30, we have:

9 + 15 + 5n = 30

5n = 6

n = 6/5 = 1 1/5 = 1 hour and 12 minutes.

Alternate Solution:

Working alone, Machine A and Machine B can complete 1/10 and 1/6 of the job in one hour, respectively. Together, they complete 1/10 + 1/6 = 16/60 = 4/15 of the job in one hour. Since they work for 3 hours, 3 x 3/15 = 12/15 = 4/5 of the job is completed and 1 - 4/5 = 1/5 of the job remains. Since Machine B completes the whole job in 6 hours, it will complete 1/5 of the job in 6 x 1/5 = 6/5 hours or, equivalently, 1 hour and 12 minutes.

Answer: B

Abhishek009 · Answer

Let total work be 30 Units (LCM of 10 & 6)

So, Efficiency of A = 3units/hr & Efficiency of B = 5units/hr , Combined efficeincy of A & B is 8 units/hr So, work completed by A & B in 3 hours is 24 units and 6 units are left for B to complete...

So, Time required by B to complete the work is  \frac{6}{5} = 1  hours  12  Minutes, Answer must be (B)

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

When working independently, machine A can complete a piece of work in

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

When working independently, machine A can complete a piece of work in

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