If w women can do a job in d days, then how many days will

I'd do this as maliyeci did above, but just wanted to point out an alternative strategy:

-if n=0, clearly the answer must be d. That gets down to A or E;

-if more women work on the task, the time required will fall, so n+d needs to be in the denominator. That gets us to A.

And of course one could plug in numbers, though that might be the most time-consuming approach.
_________________

Please note that the correct answer is A, not E.

If w women can do a job in d days, then how many days will it take (w + n) women to do the job if all the women work at the same pace?

A. \(\frac{dw}{n+w}\)

B. \(\frac{n+w}{d}\)

C. \(\frac{n+w}{dw}\)

D. \(\frac{d}{n+w}\)

E. \(\frac{d(n+w)}{w}\)

The job consists of \(wd\) units of work (1 woman does 1 unit of work in 1 day).

Thus \(w + n\) women will take \(\frac{wd}{w+n}\) days to do the job.

Answer: A.

Hope it's clear.
_________________

a women can do 1/wd part of the job in one day so that w woman can do all of the job in d days.

That makes (w+n) women can do (w+n)/wd part of the job in 1 day.

Day can do all of the job in 1/((w+n)/wd)=wd/(w+n)

A

as mentioned in the question ...work rate should be equal in both cases so:

w*d = (w+n)*X
X = no of days with (w+n) workers = {wd/w+n}

Number picking is another way to solve this.
Lets decide, that we have 5(w) women in the beggining, and 20(n) were added at the end. So w+n=25.
Lets say that 5 women can do a certain job in 50 days. Than 25 women can do same job in 50/5=10 days.
Test answers to get answer = 10 days. It is A.

Point to remember:
General formula for equating work of two groups:

(M1 D1 H1)/W1 E1 = (M2 D2 H2)/W2 E2

Where M - Number of people
D - Number of days
H - Number of hours
E - Efficiency
W - Work done
In the above problem
w women take d days:
So let w+n women take X days?

i.e w * d = (w+n) * X
or X = wd/(w+n) days
Hence Option A

w women can finish in d days.
w+n women can finish work in x days

w ----d
w+n---x
x= (w+n)d/w

E is the answer

Now try to understand this

w women take d days
1 women will take d*w days
w+n will then take d*w/w+n

Regards,
Ramandeep
_________________

Let us consider work done as 1 unit.
if w women takes d days to complete the work. then in one day they will complete 1/d work.
and 1 women can complete 1/wd of work in a day.
now we have total of n+w women now.

work done for one day by n+w women=work done for one day by one women*no of women
=1/wd *(n+w)
=(n+w)/wd
time taken to complete the work =wd/n+w

here's how I worked it out

woman rate = x; so one woman can do one job in 1/x days (inverse)
W women rate = w/x; we are told W women can do the job in d days so x/w = d
W+n women rate = (w+n)/x; x/(w+n) = z days
solve for z

x/w = d --> x = wd
wd/(w+n) = z days

My approach is similar to bunuel.

w women work for d days. Total work hours = w*d

Now w+n women will take w*d/(w+n) days to complete the w*d work hours.
Hence option A.

We are given that w women can do a job in d days. Thus, the rate of the w women is 1/d.
Next we need to determine the rate of (w + n) women. To calculate that rate, we can use the following proportion in which the value in each numerator is the number of women and the value in each denominator is the corresponding rate, and we can let r = the rate of the (w + n) women:

w/(1/d) = (w+n)/r

dw = (w+n)/r

dwr = (w + n)

r = (w + n)/dw

Finally, we need to determine the time it will take (w+n) women to complete 1 job. Since time = work/rate, we can create the following equation:

time = 1/[(w + n)/dw]

time = dw/(w + n)

Answer: A
_________________

we know number of women and days are inversely prop .
according to rule (number of women*days) =( number of women + number of extra women) * days
here to keep the work same if number of women increases days has to decreases.
so new days = wd/(w+n)

/Prabu

Can you please explain why the answer is not E.

I understand that this is an inversely proportion problem. So it wont be just (w+n)*d/w

For example, if 10 women can do the job in 10 days, how many days will 20 women take to finish the job?
The answer will be 5, not 20.

So I understand this particular concept, but I want to recognize that this is an inverse proportion problem without plugging in the number everytime, because I am trying to do it quicker.

Is there a way to recognize this? Other that just practice?

Thanks

Banuel, could you pls explain how did you proceed but step by step maybe with some example? Magda

This is a great problem to plug numbers into:

Say 10 women complete a job in 20 days

w = 10 , d = 20

Then add another 10 n women and your days will be cut in half to 10 days (you doubled the women working on the job)

Conveniently the first answer choice gives you the answer

20(10) / 10+10 = 10

Answer is A.

Ive done an analogy to facilitate.

W (women = speed)
D (days = time)

W*D = X (distance)

we want time (D) if there are more speed (more n women)

So, in analogy we have Distance/Time = Speed, Time = Distance/Speed

We know that our distance didn`t change, it`s X, or W*D.

Our speed by the way changed from W to W + N.

So substituting we have: W*D(Distance)/(W + N)(Speed) = Time

Answer A

to be honest..I hate problems with VIC's...
we have w women and d days to complete the task
the rate is thus 1/d
the rate of each woman is 1/d : w or 1/dw
now, we have w+n women
the rate of all of them will be (w+n)/dw

now, how long will these women take to finish the job?
1: (w+n)/dw or dw/(w+n)

Why dont you make your life easy and plug in values for the variables. Then use the same pluggd in valued to analyse which of the options give you the same value.

Try w=10, d=5, n=15, n+w=25, giving you the number of days for 25 women = 2 days.

Analyse the options:

A: = 2 . Keep
B: = 5. Eliminate.
C: = 0.5 .Eliminate.
D: = 0.2. Eliminate.
E: = 12.5. Eliminate.

Thus only A is left and is hence the correct answer.

You should use this approach when you are given a question full of variables and the answer choices are also in terms of those variables.
_________________