Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GPA: 3.23

Re: A husband and wife started painting their house, but husband [#permalink]
Show Tags
14 Nov 2012, 07:36
Setup the Rate Equation: \(\frac{1}{20}(d10) + \frac{1}{15}(d)=1\) \(3d15+4d=60\) \(d=\frac{75}{7}\) Answer: C
_________________
Impossible is nothing to God.



Math Expert
Joined: 02 Sep 2009
Posts: 39626

Re: A husband and wife started painting their house, but husband [#permalink]
Show Tags
08 Jul 2013, 01:09



Intern
Joined: 19 Feb 2013
Posts: 4

Re: A husband and wife started painting their house, but husband [#permalink]
Show Tags
08 Jul 2013, 05:34
Where am i going wrong?
Combined work rate= 7/60
Time H and W should have taken= 60/7
Time H & W worked together = 60/7  5= 25/7
In 25/7 days they did= 25/7 * 7/60= 5/12
Work left for wife to do= 7/12
Time taken by wife to do 7/12= 7/12 * 15= 35/4
Total Time 35/4+25/7 ?????



Math Expert
Joined: 02 Sep 2009
Posts: 39626

Re: A husband and wife started painting their house, but husband [#permalink]
Show Tags
08 Jul 2013, 05:49



Director
Joined: 17 Dec 2012
Posts: 549
Location: India

Re: A husband and wife started painting their house, but husband [#permalink]
Show Tags
08 Jul 2013, 06:48
johnnybravo86 wrote: A husband and wife, started painting their house, but husband left painting 5 days before the completion of the work. How many days will it take to complete the work, which the husband alone would have completed in 20 days and wife in 15 days?
A. 40/7 B. 50/7 C. 75/7 D. 55/7 1. In a normal scenario both the husband and wife would have taken 1/ (1/15+ 1/20) days = 60/7 days to complete the task 2. what did not happen was they definitely did not work together for 5 days. So subtract 5 days work together =5*7/60 = 7/12 th of the work 3. what did happen was the wife definitely worked alone for 5 days. So add 5 days of work of the wife = 5/15 = 1/3 rd of the work= 4/12 th of the work 4. From (2) and (3) we see 7/12 4/12 = 3/12 th or 1/4 th of the work still remains. 5. this additional 1/4 th work would have been done by both because the wife worked alone for only 5 days which we have accounted for. So time taken for this work is 1/4 * 60/7 =15/7 6. Total time taken to complete the whole work in the altered scenario is 60/7 + 15/7 = 75/7
_________________
Srinivasan Vaidyaraman Sravna http://www.sravnatestprep.com
Classroom and Online Coaching



Intern
Joined: 03 Sep 2013
Posts: 9

Re: A husband and wife started painting their house, but husband [#permalink]
Show Tags
07 Nov 2013, 12:41
Husband(working alone) completes the job in 20 days, implying a per day completion of 5% of total job Wife(working alone) completes the job in 15 days, implying a per day completion of 20/3% of total job
If we let the total no of days for work completion to be equal to 'T' days, then,
Wife works for all T days; husband works for T5 days (leaves work 5 days before completion of work)
Setting up an equation for 100% completion of work 
(T5)*5% + T*20/3% = 100%
Solving for T, T = 75/7 days



Manager
Joined: 03 Apr 2013
Posts: 179

Re: A husband and wife started painting their house, but husband [#permalink]
Show Tags
16 Nov 2013, 13:41
Hey johnnybravo86, whenever you come across such problems where you people work for different number of days or some days more or less, the best approach is to add up their individual work and not as a whole, In this problem, lets consider the work to be done as a single unit i.e. 1. now going according to the words of the question, let the wife work for x days. Thus, the husband works for x5 days. Now their respective efficiencies(fraction of work done per day) are given as, H W 1/20 1/15 now simply multiply and add The final equation is x/15 + (x5)/20 = 1 solve for x, it comes out to be 75/7, which is the OA. Kudos me!
_________________
Spread some love..Like = +1 Kudos



Senior Manager
Joined: 10 Mar 2013
Posts: 278
GMAT 1: 620 Q44 V31 GMAT 2: 690 Q47 V37 GMAT 3: 610 Q47 V28 GMAT 4: 700 Q50 V34 GMAT 5: 700 Q49 V36 GMAT 6: 690 Q48 V35 GMAT 7: 750 Q49 V42 GMAT 8: 730 Q50 V39

Re: A husband and wife started painting their house, but husband [#permalink]
Show Tags
17 Nov 2013, 06:16
t/15 + (1/20)(t5) = 1 4t/60 + 3(t5)/60 = 1 7t 15 = 60 7t = 75 t = 75/7



Manager
Joined: 26 Sep 2013
Posts: 220
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41

Re: Work & Rate problem [#permalink]
Show Tags
21 Nov 2013, 10:32
Bunuel wrote: A husband and wife, started painting their house, but husband left painting 5 days before the completion of the work. How many days will it take to complete the work, which the husband alone would have completed in 20 days and wife in 15 days? A. 40/7 B. 50/7 C. 75/7 D. 55/7
As pointed out above there are several ways to solve this problem. Below are probably two shortest approaches:
Approach #1: Rate of husband \(\frac{1}{20}\) job/day; Rate of wife \(\frac{1}{15}\) job/day; Combined rate: \(\frac{1}{20}+\frac{1}{15}=\frac{7}{60}\) job/day;
During the last 5 days, when the wife worked alone, she completed \(\frac{5}{15}=\frac{1}{3}\)rd of the job; Hence, remaining \(\frac{2}{3}\)rd of the job was done by them working together in \(time=\frac{job'}{rate}=\frac{(\frac{2}{3})}{(\frac{7}{60})}=\frac{40}{7}\) days;
Total time needed to complete the whole job: \(5+\frac{40}{7}=\frac{75}{7}\) days.
Answer: C.
Approach #2: It's based on observing the answer choices. On the PS section always look at the answer choices before you start to solve a problem. They might often give you a clue on how to approach the question.
Combined rate of the husband and wife is \(\frac{7}{60}\) job/day, which means that working together they'll complete the job in \(\frac{60}{7}\) days (time is reciprocal of rate). As they worked together only some part of the total time, then actual time would be more than \(\frac{60}{7}\) days. Only \(\frac{75}{7}\) is more than this value (answer choice C), so it must be correct.
Answer: C.
Hope it helps. Could you possibly help me figure out why my method didn't work for solving: I combined their two rates, and came up with \(\frac{7}{60}\) per day, so the whole job, combined, would have taken them \(\frac{60}{7}\), or 8 4/7 days to complete. The husband left 5 days before this, so they worked together for 3 4/7 days, or \(\frac{25}{7}\). The amount of work they completed was \(\frac{7}{60}\)* \(\frac{25}{7}\)=25/60 of the job. This leaves \(\frac{35}{60}\)of the job for the wife to complete alone. She can work at a rate of 4/60 per day. So that means she completed the remaining 35/60 in 8 3/4 days, not 5. This combined with the 3 4/7 that they worked on it together gives you a number of about 12.32, which is obviously not correct. Where did I go wrong? I'm having trouble reconciling how the wife only needed 5 days working at the rate given, when we can see how much work they did combined, and it leaves more than 5 days worth of work for her.



Math Expert
Joined: 02 Sep 2009
Posts: 39626

Re: Work & Rate problem [#permalink]
Show Tags
22 Nov 2013, 01:50
AccipiterQ wrote: Bunuel wrote: A husband and wife, started painting their house, but husband left painting 5 days before the completion of the work. How many days will it take to complete the work, which the husband alone would have completed in 20 days and wife in 15 days? A. 40/7 B. 50/7 C. 75/7 D. 55/7
As pointed out above there are several ways to solve this problem. Below are probably two shortest approaches:
Approach #1: Rate of husband \(\frac{1}{20}\) job/day; Rate of wife \(\frac{1}{15}\) job/day; Combined rate: \(\frac{1}{20}+\frac{1}{15}=\frac{7}{60}\) job/day;
During the last 5 days, when the wife worked alone, she completed \(\frac{5}{15}=\frac{1}{3}\)rd of the job; Hence, remaining \(\frac{2}{3}\)rd of the job was done by them working together in \(time=\frac{job'}{rate}=\frac{(\frac{2}{3})}{(\frac{7}{60})}=\frac{40}{7}\) days;
Total time needed to complete the whole job: \(5+\frac{40}{7}=\frac{75}{7}\) days.
Answer: C.
Approach #2: It's based on observing the answer choices. On the PS section always look at the answer choices before you start to solve a problem. They might often give you a clue on how to approach the question.
Combined rate of the husband and wife is \(\frac{7}{60}\) job/day, which means that working together they'll complete the job in \(\frac{60}{7}\) days (time is reciprocal of rate). As they worked together only some part of the total time, then actual time would be more than \(\frac{60}{7}\) days. Only \(\frac{75}{7}\) is more than this value (answer choice C), so it must be correct.
Answer: C.
Hope it helps. Could you possibly help me figure out why my method didn't work for solving: I combined their two rates, and came up with \(\frac{7}{60}\) per day, so the whole job, combined, would have taken them \(\frac{60}{7}\), or 8 4/7 days to complete. The husband left 5 days before this, so they worked together for 3 4/7 days, or \(\frac{25}{7}\). The amount of work they completed was \(\frac{7}{60}\)* \(\frac{25}{7}\)=25/60 of the job. This leaves \(\frac{35}{60}\)of the job for the wife to complete alone. She can work at a rate of 4/60 per day. So that means she completed the remaining 35/60 in 8 3/4 days, not 5. This combined with the 3 4/7 that they worked on it together gives you a number of about 12.32, which is obviously not correct. Where did I go wrong? I'm having trouble reconciling how the wife only needed 5 days working at the rate given, when we can see how much work they did combined, and it leaves more than 5 days worth of work for her. If they work together they can complete the job in 60/7 days. But if one of them does not work for all that period then the time to complete would increase. Thus you cannot say that when husband left 5 days before, then they worked together for 60/75 days. Hope it's clear.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 26 Sep 2013
Posts: 220
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41

Re: Work & Rate problem [#permalink]
Show Tags
22 Nov 2013, 17:30
Bunuel wrote: AccipiterQ wrote: Bunuel wrote: A husband and wife, started painting their house, but husband left painting 5 days before the completion of the work. How many days will it take to complete the work, which the husband alone would have completed in 20 days and wife in 15 days? A. 40/7 B. 50/7 C. 75/7 D. 55/7
As pointed out above there are several ways to solve this problem. Below are probably two shortest approaches:
Approach #1: Rate of husband \(\frac{1}{20}\) job/day; Rate of wife \(\frac{1}{15}\) job/day; Combined rate: \(\frac{1}{20}+\frac{1}{15}=\frac{7}{60}\) job/day;
During the last 5 days, when the wife worked alone, she completed \(\frac{5}{15}=\frac{1}{3}\)rd of the job; Hence, remaining \(\frac{2}{3}\)rd of the job was done by them working together in \(time=\frac{job'}{rate}=\frac{(\frac{2}{3})}{(\frac{7}{60})}=\frac{40}{7}\) days;
Total time needed to complete the whole job: \(5+\frac{40}{7}=\frac{75}{7}\) days.
Answer: C.
Approach #2: It's based on observing the answer choices. On the PS section always look at the answer choices before you start to solve a problem. They might often give you a clue on how to approach the question.
Combined rate of the husband and wife is \(\frac{7}{60}\) job/day, which means that working together they'll complete the job in \(\frac{60}{7}\) days (time is reciprocal of rate). As they worked together only some part of the total time, then actual time would be more than \(\frac{60}{7}\) days. Only \(\frac{75}{7}\) is more than this value (answer choice C), so it must be correct.
Answer: C.
Hope it helps. Could you possibly help me figure out why my method didn't work for solving: I combined their two rates, and came up with \(\frac{7}{60}\) per day, so the whole job, combined, would have taken them \(\frac{60}{7}\), or 8 4/7 days to complete. The husband left 5 days before this, so they worked together for 3 4/7 days, or \(\frac{25}{7}\). The amount of work they completed was \(\frac{7}{60}\)* \(\frac{25}{7}\)=25/60 of the job. This leaves \(\frac{35}{60}\)of the job for the wife to complete alone. She can work at a rate of 4/60 per day. So that means she completed the remaining 35/60 in 8 3/4 days, not 5. This combined with the 3 4/7 that they worked on it together gives you a number of about 12.32, which is obviously not correct. Where did I go wrong? I'm having trouble reconciling how the wife only needed 5 days working at the rate given, when we can see how much work they did combined, and it leaves more than 5 days worth of work for her. If they work together they can complete the job in 60/7 days. But if one of them does not work for all that period then the time to complete would increase. Thus you cannot say that when husband left 5 days before, then they worked together for 60/75 days. Hope it's clear. absolutely, thank you!



Intern
Joined: 21 May 2013
Posts: 10

Re: A husband and wife started painting their house, but husband [#permalink]
Show Tags
27 Apr 2014, 10:46
johnnybravo86 wrote: A husband and wife, started painting their house, but husband left painting 5 days before the completion of the work. How many days will it take to complete the work, which the husband alone would have completed in 20 days and wife in 15 days?
A. 40/7 B. 50/7 C. 75/7 D. 55/7 Here's my simple solution. Let total time taken for the job together = T Husband worked for days = T5 Wife worked for days = T Then, according to individual rates, (T5)/20 + T/15 = 1 => 35T = 375 or, T = 75/7 Ans. C. 75/7



Senior Manager
Joined: 28 Apr 2014
Posts: 282

Re: Work & Rate problem [#permalink]
Show Tags
28 Apr 2014, 03:39
Bunuel wrote: A husband and wife, started painting their house, but husband left painting 5 days before the completion of the work. How many days will it take to complete the work, which the husband alone would have completed in 20 days and wife in 15 days? A. 40/7 B. 50/7 C. 75/7 D. 55/7
As pointed out above there are several ways to solve this problem. Below are probably two shortest approaches:
Approach #1: Rate of husband \(\frac{1}{20}\) job/day; Rate of wife \(\frac{1}{15}\) job/day; Combined rate: \(\frac{1}{20}+\frac{1}{15}=\frac{7}{60}\) job/day;
During the last 5 days, when the wife worked alone, she completed \(\frac{5}{15}=\frac{1}{3}\)rd of the job; Hence, remaining \(\frac{2}{3}\)rd of the job was done by them working together in \(time=\frac{job'}{rate}=\frac{(\frac{2}{3})}{(\frac{7}{60})}=\frac{40}{7}\) days;
Total time needed to complete the whole job: \(5+\frac{40}{7}=\frac{75}{7}\) days.
Answer: C.
Approach #2: It's based on observing the answer choices. On the PS section always look at the answer choices before you start to solve a problem. They might often give you a clue on how to approach the question.
Combined rate of the husband and wife is \(\frac{7}{60}\) job/day, which means that working together they'll complete the job in \(\frac{60}{7}\) days (time is reciprocal of rate). As they worked together only some part of the total time, then actual time would be more than \(\frac{60}{7}\) days. Only \(\frac{75}{7}\) is more than this value (answer choice C), so it must be correct.
Answer: C.
Hope it helps. Approach # 2 definitely the smart way to think and work over here !!



Current Student
Status: Applied
Joined: 02 May 2014
Posts: 168
Location: India
Concentration: Operations, General Management
Schools: Tulane '18 (A), Tippie '18 (D), Moore '18, Katz '18 (D), UCSD '18, Madison '18, Olin '18 (S), Simon '18, Desautels '18 (I), Sauder '18 (S), Terry '18 (WL), GWU '18, Neeley '18 (WL), Weatherhead '18 (S), Fox(Temple)'18, Eller FT'18 (A), Schulich Sept"18 (S)
GPA: 3.35
WE: Information Technology (Computer Software)

Re: A husband and wife started painting their house, but husband [#permalink]
Show Tags
09 Mar 2015, 06:41
In how many days it will finish the work . together they can finish in 60/7 days, but someone left the works with 5 days to spare..Now it means it will take more than 60/7 only option giving is 75/7 days hence this is the answer.Hope this helps.



Intern
Joined: 29 Sep 2012
Posts: 1

Re: A husband and wife started painting their house, but husband [#permalink]
Show Tags
11 Mar 2015, 10:20
tkarthi4u wrote: H take 20 days = 1 W take 15 days = 1 H one day work = 1/20 and W one day work = 1/15
H + W one day work = 1/20 + 1/15 = 7/60.
In a total of T day H+W worked for T5 and W alone for 5
(7/60) (T5) + 1/15 * 5 = 1 therefore T = 75/7
Ans : C If we have a look at the problem then we come to know that the work was completed in T days when both worked together. But when Husband moves out then the remaining work must have taken more than 5 days to complete as earlier it was both husband and wife and now it is only wife.The work would have got completed in 5 days provide both of them have worked.Also it is not mentioned nywhere in the problem that the work gets completed on time.Please correct me if I am wrong



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15939

Re: A husband and wife started painting their house, but husband [#permalink]
Show Tags
22 Mar 2016, 13:36
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Director
Joined: 07 Dec 2014
Posts: 710

A husband and wife started painting their house, but husband [#permalink]
Show Tags
22 Mar 2016, 23:54
let d=total days to complete work (d5)(7/60)+5(4/60)=1 7d=75 d=75/7 days



Intern
Joined: 07 Mar 2016
Posts: 16
Location: Indonesia
GPA: 3.06

Re: A husband and wife started painting their house, but husband [#permalink]
Show Tags
27 Mar 2016, 07:33
bharathh wrote: With the answer choices given there's a faster way.
There is no need to solve the whole thing.
Using the rate eqn for combined work... 1/20 + 1/15 = 7/60
So it would take 60/7 days combined. If the Husband quits working a few days earlier... total time is going to be > 60/7. There is only one value > 60/7 so answer is 75/7 absolutely correct ! thanks



Intern
Joined: 09 Jul 2015
Posts: 29
Location: India
Concentration: Finance
GMAT 1: 690 Q50 V32 GMAT 2: 750 Q51 V40
GPA: 3

Re: A husband and wife started painting their house, but husband [#permalink]
Show Tags
02 May 2016, 06:00
Bunuel wrote: Bumping for review and further discussion*. Get a kudos point for an alternative solution! *New project from GMAT Club!!! Check HEREHi Bunuel Please help !! Together they will finish the work in 60/7 days Husband left 5 days before the completion. Therefore, he left 5/20 = 1/4 of the work for his wife. Wife will complete 1/4 of the work in 15/4 days Total days needed to complete the work = 60/7 + 15/4 = 345/28 days



Verbal Forum Moderator
Joined: 02 Aug 2009
Posts: 4559

Re: A husband and wife started painting their house, but husband [#permalink]
Show Tags
02 May 2016, 06:33
subhamgarg91 wrote: Bunuel wrote: Bumping for review and further discussion*. Get a kudos point for an alternative solution! *New project from GMAT Club!!! Check HEREHi Bunuel Please help !! Together they will finish the work in 60/7 days Husband left 5 days before the completion. Therefore, he left 5/20 = 1/4 of the work for his wife. Wife will complete 1/4 of the work in 15/4 days Total days needed to complete the work = 60/7 + 15/4 = 345/28 days HI, the way you have calculated the last 5 days work is ' in the scenario where ONLY the husband was working and he left 5 days before he would have finished the work alone.. Remember both are working..and last 5 days only the wife works to finish the job.. in 5 days she would do 5/15 of the work.. so 2/3rd work was finished by BOTH with a speed of 7/60th of work per hour
_________________
Absolute modulus :http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html




Re: A husband and wife started painting their house, but husband
[#permalink]
02 May 2016, 06:33



Go to page
Previous
1 2 3
Next
[ 46 posts ]




