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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
_________________

Re: A husband and wife started painting their house, but husband [#permalink]

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07 Nov 2013, 11:41

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 T-5 days (leaves work 5 days before completion of work)

Setting up an equation for 100% completion of work -

Re: A husband and wife started painting their house, but husband [#permalink]

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16 Nov 2013, 12:41

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 x-5 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 + (x-5)/20 = 1 solve for x, it comes out to be 75/7, which is the OA. Kudos me!
_________________

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.

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 60/7-5 days.

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 60/7-5 days.

Re: A husband and wife started painting their house, but husband [#permalink]

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27 Apr 2014, 09:46

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 = T-5 Wife worked for days = T

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 !!

Re: A husband and wife started painting their house, but husband [#permalink]

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09 Mar 2015, 05:41

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.

Re: A husband and wife started painting their house, but husband [#permalink]

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11 Mar 2015, 09:20

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 T-5 and W alone for 5

(7/60) (T-5) + 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

Re: A husband and wife started painting their house, but husband [#permalink]

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27 Mar 2016, 06:33

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

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
_________________

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