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# When A works alone, it takes 14hrs, and when A works with B together,

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When A works alone, it takes 14hrs, and when A works with B together,  [#permalink]

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09 Aug 2017, 04:29
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97% (01:12) correct 3% (00:00) wrong based on 54 sessions

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When A works alone, it takes 14hrs, and when A works with B together, it takes 10hrs. How many hours does it take B to work alone?

A. 30hrs
B. 33hrs
C. 35hrs
D. 37hrs
E. 40hrs

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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 17 May 2015 Posts: 249 When A works alone, it takes 14hrs, and when A works with B together, [#permalink] ### Show Tags Updated on: 10 Aug 2017, 00:21 MathRevolution wrote: When A works alone, it takes 14hrs, and when A works with B together, it takes 10hrs. How many hours does it take B to work alone? A. 30hrs B. 33hrs C. 35hrs D. 37hrs E. 40hrs Hi, Note: Consider total amount of work as LCM of no. of hours required by different persons. In this case, let's assume total amount of work = 70 units (LCM (14,10) = 70) Rate of A work = 70/14 = 5 units/hr Rate of A+B work = 70/10 = 7 units/hr Rate of B work = 7 - 5 = 2 units/hr The total amount of time required to complete the work by B = 70/2 = 35 hrs. Answer: (C) Thanks. Originally posted by ganand on 09 Aug 2017, 04:39. Last edited by ganand on 10 Aug 2017, 00:21, edited 1 time in total. Intern Joined: 03 Feb 2015 Posts: 5 Re: When A works alone, it takes 14hrs, and when A works with B together, [#permalink] ### Show Tags 09 Aug 2017, 05:20 Lets arrange the Information and assume that 1 unit of work needs to be done. Work = Rate * Time A: 1 = * 14 B: 1 = * T A+B: 1 = * 10 Now we fill in what we can deduct Work = Rate * Time A: 1 = 1/14 * 14 B: 1 = 1/T * T A+B: 1 = 1/10 * 10 What we need is T. If we add the rates of A and B we get the combined rate A+B. (1/14) + (1/T) = (1/10) =>(T+14 / 14T) = (1/10) =>T+14 = (14T/10) =>10T + 140 = 14T =>140 = 4T =>T = 35 Answer C Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4471 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: When A works alone, it takes 14hrs, and when A works with B together, [#permalink] ### Show Tags 09 Aug 2017, 09:03 MathRevolution wrote: When A works alone, it takes 14hrs, and when A works with B together, it takes 10hrs. How many hours does it take B to work alone? A. 30hrs B. 33hrs C. 35hrs D. 37hrs E. 40hrs Let the total work be = 70 Efficiency of A = 5 Efficiency of A + B = 7 So, Efficiency of B = 2 So, Time taken by B to work alone is $$\frac{70}{2}$$ = $$35$$ hours.. Thus, 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 ) Senior SC Moderator Joined: 22 May 2016 Posts: 2730 When A works alone, it takes 14hrs, and when A works with B together, [#permalink] ### Show Tags 09 Aug 2017, 09:10 MathRevolution wrote: When A works alone, it takes 14hrs, and when A works with B together, it takes 10hrs. How many hours does it take B to work alone? A. 30hrs B. 33hrs C. 35hrs D. 37hrs E. 40hrs There are a few ways to solve these problems. If possible, I find adding rates the easiest. "It" is one job, or one unit of work. (Rate of A and B together) - (rate of A) = (rate of B) $$\frac{1}{10}$$ - $$\frac{1}{14}$$ =$$\frac{(14 - 10)}{140}$$ = $$\frac{4}{140}$$ = $$\frac{1}{35}$$ --> B's rate When work unit is one, flip the rate to get the time: 1/(1/35) = 35 Answer C _________________ Listen, are you breathing just a little, and calling it a life? -- Mary Oliver For practice SC questions go to SC Butler, here. Please DO NOT write short answers in your verbal posts! Such answers will be deleted. Manager Joined: 07 Jun 2017 Posts: 100 Re: When A works alone, it takes 14hrs, and when A works with B together, [#permalink] ### Show Tags 09 Aug 2017, 19:39 Abhishek009 wrote: MathRevolution wrote: When A works alone, it takes 14hrs, and when A works with B together, it takes 10hrs. How many hours does it take B to work alone? A. 30hrs B. 33hrs C. 35hrs D. 37hrs E. 40hrs Let the total work be = 70 Efficiency of A = 5 Efficiency of A + B = 7 So, Efficiency of B = 2 So, Time taken by B to work alone is $$\frac{70}{2}$$ = $$35$$ hours.. Thus, answer must be (C) Hello, How do you assume A= 5? Thank you very much Senior PS Moderator Joined: 26 Feb 2016 Posts: 3386 Location: India GPA: 3.12 Re: When A works alone, it takes 14hrs, and when A works with B together, [#permalink] ### Show Tags 09 Aug 2017, 20:04 Hi pclawong, It is not so much as assumption in this case. Here, the total units of work is 70 units and since A (when working alone) does the work in 14 hours, A's efficieny is 70/14 = 5 units Similarly, Since both do the work in 10 hours, their combined efficiency is 7 units. This makes the efficiency of B(2 units), and the time it takes him to complete the work 35 hours(Option C) Hope that helps you! _________________ You've got what it takes, but it will take everything you've got Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7343 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: When A works alone, it takes 14hrs, and when A works with B together, [#permalink] ### Show Tags 11 Aug 2017, 01:03 ==> For work rate questions, you solve “together and alone” reciprocally. It takes A 14hrs alone, and if you set the hours it took B to work alone as B hrs, from $$(\frac{1}{14})+(\frac{1}{B})=\frac{1}{10}$$ and $$\frac{1}{B}=(\frac{1}{10})-(\frac{1}{14})=\frac{1}{35}$$, you get $$B=35$$. The answer is C. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: When A works alone, it takes 14hrs, and when A works with B together,   [#permalink] 11 Aug 2017, 01:03
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# When A works alone, it takes 14hrs, and when A works with B together,

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