GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 06 Apr 2020, 06:00

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Two workers A and B are engaged to do a work. A working alone takes 8

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 62531
Two workers A and B are engaged to do a work. A working alone takes 8  [#permalink]

### Show Tags

24 Jan 2020, 02:05
00:00

Difficulty:

45% (medium)

Question Stats:

71% (02:44) correct 29% (02:49) wrong based on 72 sessions

### HideShow timer Statistics

Two workers A and B are engaged to do a work. A working alone takes 8 hours more to complete the job than if both worked together. If B worked alone, he would need 4.5 hours more to complete the job than they both working together. What time would they take to do the work together ?

A. 4 hours
B. 5 hours
C. 6 hours
D. 7 hours
E. 8 hours

Are You Up For the Challenge: 700 Level Questions

_________________
Director
Joined: 16 Jan 2019
Posts: 555
Location: India
Concentration: General Management
WE: Sales (Other)
Two workers A and B are engaged to do a work. A working alone takes 8  [#permalink]

### Show Tags

24 Jan 2020, 02:38
1
Bunuel wrote:
Two workers A and B are engaged to do a work. A working alone takes 8 hours more to complete the job than if both worked together. If B worked alone, he would need 4.5 hours more to complete the job than they both working together. What time would they take to do the work together ?

A. 4 hours
B. 5 hours
C. 6 hours
D. 7 hours
E. 8 hours

Are You Up For the Challenge: 700 Level Questions

$$(A+B)t=1$$ or $$(A+B)=\frac{1}{t}$$
$$A(t+8)=1$$ or $$A=\frac{1}{t+8}$$
$$B(t+4.5)=1$$ or $$B=\frac{1}{t+4.5}$$

$$\frac{1}{t+8}+\frac{1}{t+4.5}=\frac{1}{t}$$

$$\frac{1}{t+4.5}=\frac{1}{t}-\frac{1}{t+8}$$

$$\frac{1}{t+4.5}=\frac{t+8-t}{t(t+8)}$$

$$t(t+8)=8(t+4.5)$$

$$t^2+8t=8t+36$$

$$t^2=36$$

$$t=6$$

GMAT Tutor
Status: Entrepreneur | GMAT, GRE, CAT, SAT, ACT coach & mentor | Founder @CUBIX | Edu-consulting | Content creator
Joined: 26 Jun 2014
Posts: 134
GMAT 1: 740 Q51 V39
Two workers A and B are engaged to do a work. A working alone takes 8  [#permalink]

### Show Tags

24 Jan 2020, 04:35
Question:
Two workers A and B are engaged to do a work. A working alone takes 8 hours more to complete the job than if both worked together. If B worked alone, he would need 4.5 hours more to complete the job than they both working together. What time would they take to do the work together?

Solution:
Let A and B together take t hours to complete the work.
Thus, time taken by A = (t + 8) hrs and time taken by B = (t + 4.5) hrs

Thus, we can say that:
Work done by (A and B) in t hours = Work done by A in (t + 8) hours = Total work
=> (Work done by A in t hrs) + (Work done by B in t hrs) = (Work done by A in t hrs) + (Work done by A in 8 hrs)

Cancelling the (Work done by A in t hrs) from both sides:
(Work done by B in t hrs) = (Work done by A in 8 hrs)
=> Work done by B in 1 hr = Work done by A in (8/t) hrs ... (i)

Similarly, we have:
Work done by (A and B) in t hours = Work done by B in (t + 4.5) hours = Total work
=> (Work done by A in t hrs) + (Work done by B in t hrs) = (Work done by B in t hrs) + (Work done by B in 4.5 hrs)

Cancelling the (Work done by B in t hrs) from both sides:
(Work done by A in t hrs) = (Work done by B in 4.5 hrs)
=> Work done by B in 1 hr = Work done by A in (t/4.5) hrs ... (ii)

Thus, from (i) and(ii):
8/t = t/4.5

=> $$t^2 = 36$$
=> t = 6 hrs

Alternate approach
Let time taken by A and B together be t hours
Thus, time taken by A = (t + 8) hrs and time taken by B = (t + 4.5) hrs

thus, equating work done by A and B in 1 hour:
1/(t + 8) + 1/(t + 4.5) = 1/t

Solving, we get: t = 6 hours
_________________
Sujoy Kumar Datta
Director - CUBIX Educational Institute Pvt. Ltd. (https://www.cubixprep.com)
IIT Kharagpur, TU Dresden Germany
GMAT - Q51 & CAT (MBA @ IIM) 99.98 Overall with 99.99 QA
_________
Feel free to talk to me about GMAT & GRE | Ask me any question on QA (PS / DS)
Let's converse!
Skype: sk_datta
Alt. Email: sujoy.datta@gmail.com
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4874
Location: India
GPA: 3.5
Re: Two workers A and B are engaged to do a work. A working alone takes 8  [#permalink]

### Show Tags

24 Jan 2020, 08:58
1
Bunuel wrote:
Two workers A and B are engaged to do a work. A working alone takes 8 hours more to complete the job than if both worked together. If B worked alone, he would need 4.5 hours more to complete the job than they both working together. What time would they take to do the work together ?

A. 4 hours
B. 5 hours
C. 6 hours
D. 7 hours
E. 8 hours

Are You Up For the Challenge: 700 Level Questions

A short little formula exists which can solve it in 10 secs -

$$\sqrt{8*4.5}$$

$$= \sqrt{36}$$

$$= 6$$ , Answer must be (C)
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
VP
Joined: 24 Nov 2016
Posts: 1338
Location: United States
Re: Two workers A and B are engaged to do a work. A working alone takes 8  [#permalink]

### Show Tags

28 Jan 2020, 06:49
Bunuel wrote:
Two workers A and B are engaged to do a work. A working alone takes 8 hours more to complete the job than if both worked together. If B worked alone, he would need 4.5 hours more to complete the job than they both working together. What time would they take to do the work together ?

A. 4 hours
B. 5 hours
C. 6 hours
D. 7 hours
E. 8 hours

r=w/t

(a+b)=1/t
a=1/t+8
b=1/t+4.5
(1/t+8)+(1/t+4.5)=1/t
2t^2+12.5t=t^2+12.5t+36
t^2=36 (t>0) t=6

Ans (C)
VP
Joined: 18 Dec 2017
Posts: 1272
Location: United States (KS)
GMAT 1: 600 Q46 V27
Re: Two workers A and B are engaged to do a work. A working alone takes 8  [#permalink]

### Show Tags

11 Feb 2020, 17:48
Quote:

A short little formula exists which can solve it in 10 secs -

$$\sqrt{8*4.5}$$

$$= \sqrt{36}$$

$$= 6$$ , Answer must be (C)

Abhishek009

Any theory or links on how this is achievable and in what conditions it usually works?

Thank you!
_________________
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long

Why You Don’t Deserve A 700 On Your GMAT

Learn from the Legend himself: All GMAT Ninja LIVE YouTube videos by topic
You are missing on great learning if you don't know what this is: Project SC Butler
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9960
Location: United States (CA)
Re: Two workers A and B are engaged to do a work. A working alone takes 8  [#permalink]

### Show Tags

16 Feb 2020, 07:03
1
Bunuel wrote:
Two workers A and B are engaged to do a work. A working alone takes 8 hours more to complete the job than if both worked together. If B worked alone, he would need 4.5 hours more to complete the job than they both working together. What time would they take to do the work together ?

A. 4 hours
B. 5 hours
C. 6 hours
D. 7 hours
E. 8 hours

Are You Up For the Challenge: 700 Level Questions

Let’s let n = the number of hours it takes to complete the job when A and B work together; thus, their combined rate is 1/n. Since A alone takes 8 hours more than if they work together, then A’s rate is 1/(n + 8). And since B alone takes 4.5 hours more than if they work together, then B’s rate is 1/(n + 4.5).

Thus, , we can create the rate equation:

1/(n + 8) + 1/(n + 4.5) = 1/n

Multiplying by n(n + 8)(n + 4.5), we have:

n(n + 4.5) + n(n + 8) = (n + 8)(n + 4.5)

n^2 + 4.5n + n^2 + 8n = n^2 + 4.5n + 8n + 36

2n^2 + 12.5n = n^2 + 12.5n + 36

n^2 = 36

n = 6 or -6

Since n can’t be negative, n = 6.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
197 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4874
Location: India
GPA: 3.5
Re: Two workers A and B are engaged to do a work. A working alone takes 8  [#permalink]

### Show Tags

20 Feb 2020, 07:21
TheNightKing wrote:
Quote:

A short little formula exists which can solve it in 10 secs -

$$\sqrt{8*4.5}$$

$$= \sqrt{36}$$

$$= 6$$ , Answer must be (C)

Abhishek009

Any theory or links on how this is achievable and in what conditions it usually works?

Thank you!

RESPONDING TO A PM IN THIS REGARD -

Quote:
Two workers A and B are engaged to do a work. A working alone takes a hours more to complete the job than if both worked together. If B worked alone, he would need b hours more to complete the job than they both working together. What time would they take to do the work together ?

Time required to complete the task will be $$\sqrt{ab}$$

It can be applied to all such cases without any restriction !!
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Re: Two workers A and B are engaged to do a work. A working alone takes 8   [#permalink] 20 Feb 2020, 07:21
Display posts from previous: Sort by