Kindly solve this work question
 

Aoa,

Kindly solve this question. In this question, two different people are doing the same work, and this is confusing me in its solution :thinking

If 3 men or 6 boys can do a work in 20 days, then 6 men and 8 boys shall take:

A. 6 days.
B. 8 days.
C. 9 days.
D. 20 days.

P.S: Quick and detailed reply would be highly appreciated. Thanks in anticipation.

Regards.

my answer is 7.5 (approx 8 because 8 is not in the options)
the number of men and boys is increasing so they will be doing the work in less days, therefore men and boys are at inverse with days (so it is indirect proportion)

having a test tomorrow?

Solution
 

Ans: Given, work can be done by:
3*20 = 60 man-days
or
6*20 = 120 boy-days
therefore
60 md = 120 b.d

divide by 60
md = 2bd
:
how many days will 6 men and 8 boys take to do the same work?
let d = no. days to accomplish this in terms of man-days
we know that 8bd = 4 md; therefore
6d + 4d = 60
10d = 60
d = 6 days for 6 men and 8 boys to do the job

[QUOTE=Mashaaal;862532]my answer is 7.5 (approx 8 because 8 is not in the options)
the number of men and boys is increasing so they will be doing the work in less days, therefore men and boys are at inverse with days (so it is indirect proportion)[/QUOTE]

Yup, I have a test tomorrow. I have done with the other part of mathematics but stuck in this weird question :mad:

8 is among the options. :) Btw, I know that it's indirect proportion but it's really confusing and I think this question is solved by a linear equation. Let's see if somebody else knows it. :glare:

[QUOTE=FAHEEM ULLAH KHAN MAHSUD;862535]Ans: Given, work can be done by:
3*20 = 60 man-days
or
6*20 = 120 boy-days
therefore
60 md = 120 b.d

divide by 60
md = 2bd
:
how many days will 6 men and 8 boys take to do the same work?
let d = no. days to accomplish this in terms of man-days
we know that 8bd = 4 md; therefore
6d + 4d = 60
10d = 60
d = 6 days for 6 men and 8 boys to do the job[/QUOTE]

Jazak'ALLAH khairan.

Thanks a bunch bro but I didn't understand the 2nd part of your solution. Could you please throw some light on this: we know that 8bd = 4 md; therefore
6d + 4d = 60
10d = 60
d = 6 days for 6 men and 8 boys to do the job

How did you get 4md and where is 8bd after that step ?

oh. it is boys or men,,, and i am taking it as boys and men, sorry,,
but yes you have written it both ways,, once you have written or' and then and'???? confused

@Mishal

Mam, I have attempted by your method and it gives 7.5 that somehow makes '8' the right answer. But, still I am not satisfied and I think Faheem's method and answer is right.

@Faheem

Kindly reply. It's getting late.

[QUOTE=RMKamran;862530]Aoa,

Kindly solve this question. In this question, two different people are doing the same work, and this is confusing me in its solution :thinking

If 3 men or 6 boys can do a work in 20 days, then 6 men and 8 boys shall take:

A. 6 days.
B. 8 days.
C. 9 days.
D. 20 days.

P.S: Quick and detailed reply would be highly appreciated. Thanks in anticipation.

Regards.[/QUOTE]

[QUOTE=Mashaaal;862532]my answer is 7.5 (approx 8 because 8 is not in the options)
the number of men and boys is increasing so they will be doing the work in less days, therefore men and boys are at inverse with days (so it is indirect proportion)

having a test tomorrow?[/QUOTE]

3 men = 6 boys
Then, 1 boy = 3/6 men = 1/2 men
8 boys = 1/2 × 8 men = 4 men
Then, 6 men + 8 boys = 6 + 4 men = 10 men
work done = 3 men × 20days
That is, 3 × 20 = 10 × (required days)
3 × 2 = 1 × (required days)
so (required days) =6.

[QUOTE=Z Ali S;862575]3 men = 6 boys
Then, 1 boy = 3/6 men = 1/2 men
8 boys = 1/2 × 8 men = 4 men
Then, 6 men + 8 boys = 6 + 4 men = 10 men
work done = 3 men × 20days
That is, 3 × 20 = 10 × (required days)
3 × 2 = 1 × (required days)
so (required days) =6.[/QUOTE]

:blink

can you please express your solution in words ? I didn't understand it.

Pipe A can fill a tank in 3minutes, whereas b can fill it in 4minites. How long would it take both pipes working together to fill it?

What is logic of inverse in ans? can one one plz explain it?

Thanks in anticipation

[QUOTE=RMKamran;862530]Aoa,

Kindly solve this question. In this question, two different people are doing the same work, and this is confusing me in its solution :thinking

If 3 men or 6 boys can do a work in 20 days, then 6 men and 8 boys shall take:

A. 6 days.
B. 8 days.
C. 9 days.
D. 20 days.

P.S: Quick and detailed reply would be highly appreciated. Thanks in anticipation.

Regards.[/QUOTE]

1 Man = 2 Boys

Total Boy-days required to complete the task = 6 boys x 20 days = 120 Boy-days
120 days are required by one boy to complete the task.

Now come to the 'then' part.

because
6 men = 12 boys

therefore,

6 men + 8 boys = 12 boys + 8 boys = 20 boys

Now days required to complete the task = 120 boy-days /20 boys = 6 days


120 days are required by one boy to complete the task so the days required by 20 boys will be 120/20 = 6 days.

You can also solve by pursuing with the men instead of boys, i.e. 1 man = 2 boys.