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

It is currently 29 Mar 2020, 17:32

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Tina can do as much work in 2 days as Leena can do in 3 days and Leena

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 62289
Tina can do as much work in 2 days as Leena can do in 3 days and Leena  [#permalink]

Show Tags

New post 19 Jan 2020, 23:31
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

45% (03:01) correct 55% (03:33) wrong based on 22 sessions

HideShow timer Statistics

Tina can do as much work in 2 days as Leena can do in 3 days and Leena can do as much work in 4 days as Meena can do in 5 days. If all three work together, they take 20 days to finish a work. How long would Leena take to finish the work if she works alone?

A. 50 days
B. 60 days
C. 66 days
D. 72 days
E. 75 days

_________________
GMAT Tutor
User avatar
B
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
Re: Tina can do as much work in 2 days as Leena can do in 3 days and Leena  [#permalink]

Show Tags

New post 20 Jan 2020, 00:53
1
Question)
Tina can do as much work in 2 days as Leena can do in 3 days and Leena can do as much work in 4 days as Meena can do in 5 days. If all three work together, they take 20 days to finish a work. How long would Leena take to finish the work if she works alone?

Solution:
Work by Tina in 2 days = Work by Leena in 3 days
Work by Leena in 4 days = Work by Meena in 5 days

Combining: Work by Tina in 8 days = Work by Leena in 12 days = Work by Meena in 15 days

Let the work be the LCM (least common multiple) of 8, 12, 15 = 120 units
=> Work by Tina in 8 days = Work by Leena in 12 days = Work by Meena in 15 days = 120 units

=> Work by Tina in 1 day = 15 units; Work by Leena in 1 day = 10 units; Work by Meena in 1 day = 8 units
=> Work done by all three together in 1 day = 33 units
=> Work done by all three together in 20 days (total work duration) = 660 units

Thus, total work volume is of 660 units
=> Time taken by Leena to complete the work = 660/10 = 66 days

Answer C
_________________
Sujoy Kumar Datta
Director - CUBIX Educational Institute Pvt. Ltd. (https://www.cubixprep.com)
IIT Kharagpur, TU Dresden Germany
Linked-in: https://www.linkedin.com/in/sujoy-kumar-datta/
GMAT - Q51 & CAT (MBA @ IIM) 99.98 Overall with 99.99 QA
Ask me anything about GMAT Quant
_________
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
GMATWhiz Representative
User avatar
G
Joined: 07 May 2019
Posts: 391
Location: India
Re: Tina can do as much work in 2 days as Leena can do in 3 days and Leena  [#permalink]

Show Tags

New post 09 Feb 2020, 23:49
Bunuel wrote:
Tina can do as much work in 2 days as Leena can do in 3 days and Leena can do as much work in 4 days as Meena can do in 5 days. If all three work together, they take 20 days to finish a work. How long would Leena take to finish the work if she works alone?

A. 50 days
B. 60 days
C. 66 days
D. 72 days
E. 75 days


Solution


    • Let us assume that the time taken by Leena to finish the required work alone is x days.
    • Also, let us assume that the working rate of Tina, Leena and Meena be t, l, and m units per days.
    • Now, Tina can do as much work in 2 days as Leena can do in 3 days
      o \(2t =3l ⟹ t = \frac{3l}{2} …………. Eq. (i)\)
    • And, Leena can do as much work in 4 days as Meena can do in 5 days.
      o So, \(4l =5m ⟹ m = \frac{4l}{5} …………. Eq. (ii)\)
    • Now, work done by Leena in x days = work done by all three in 20 days
      o \(l*x = (t + l + m) *20\)
      o Substituting the values of t and m from Eq.(i) and Eq(ii) into the above equation,
         \(l*x = (\frac{3l}{2} + l + \frac{4l}{5})*20\)
         Or, \(l*x = \frac{(15l + 10l + 8l)}{10}*20\)
         Or, \(x = 66\) days.
Thus, the correct answer is Option C.
_________________

GMAT Prep truly Personalized using Technology


Prepare from an application driven course that serves real-time improvement modules along with a well-defined adaptive study plan. Start a free trial to experience it yourself and get access to 25 videos and 300 GMAT styled questions.

Helpful Links


Score Improvement Strategy: How to score Q50+ on GMAT | 5 steps to Improve your Verbal score
Study Plan Articles: 3 mistakes to avoid while preparing | How to create a study plan? | The Right Order of Learning | Importance of Error Log
Helpful Quant Strategies: Filling Spaces Method | Avoid Double Counting in P&C | The Art of Not Assuming anything in DS | Number Line Method
Key Verbal Techniques: Plan-Goal Framework in CR | Quantifiers the tiny Game-changers | Countable vs Uncountable Nouns | Tackling Confusing Words in Main Point
GMAT Club Bot
Re: Tina can do as much work in 2 days as Leena can do in 3 days and Leena   [#permalink] 09 Feb 2020, 23:49
Display posts from previous: Sort by

Tina can do as much work in 2 days as Leena can do in 3 days and Leena

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne