It takes 16 days for 48 women to complete a job that

Question

It takes 16 days for 48 women to complete a job that requires 16 men to complete in 24 days. 12 men initiated the work and after 14 days 12 women joined them. How many days will they together take to complete the job?

....i always get stuck with such probs ?? a basic formula & more sample questions on these types...please

thanks in advance

twixt · Answer

Sushom,

In this kind of question, always go back to the job (=J) fraction :

Each man completes J/(16.24) per day
Each woman completes J/(48.16) per day

12 men initiated the work during 14 days = J.12.14/(16.24) = A
12 women joined them during X more days = 12.X.J(1/(16.24)+1/(48.16)) = B

then just considering A+B = J you find X=12

ywilfred · Answer

It takes 16 days for the women to complete the work. So in one day, 1/16 of the work is completed. Since there are 48 women, each women does 1/(16*48) = 1/768 of the work in one day

It takes 24 days for the men to complete the work. SO in one day, 1/24 of the work is completed. Since there are 16 men, each men does 1/(24*16) = 1/384 of the work in one day.

We're told 12 men initiated the work and works for 14 days. So in one day, 1/384 * 12 = 1/32 of the work is done. For 14 days, 1/32 * 14 = 7/16 of the work is done. So 9/16 of the work is unfinished.

We're told 12 women joins the team. 12 women will finish 1/768 * 12 = 1/64 of the work in one day. 12 men will finish 1/32 of the work in one day. So the combined rate in one day = 1/64 + 1/32 = 3/64 of the work in one day.

The number of days needed to complete the remaining 9/16 of the work is therefore 9/16 * 64/3 = 12 days.

The total number of days = 14 + 12 = 26 days.

gsr · Answer

In 1 day, a woman can do -> 1/16*48 of the work
In 1 day, a man can do -> 1/16*24 of the work

12 men working for 14 days do, 12*14/(16*24) = 7/16 or work.

So the amount of remaining work that needs to be done by 12 men and 12 women is 1 - 7/16 = 9/16

In 1 day, a M and a W can do, (1/16*48 + 1/16*24) = 3/64 of the work.
So to complete 9/16 of the work, they will take = (64/3)*(9/16) =  12 additional days

sushom101 · Answer

thanks guys...though i feel its time consuming...will take me easily 3 to 4 mins.

GMATT73 · Answer

A different approach:

X= time for 1 man to do the job
Y= time for one woman to the job

48Y*16=1 
16X*24=1
therefore, 48Y*16=16X*24 ---> X=2Y (Equation 1)

12X*14+(12X+12Y)T=16X*24 (Whereas T=Time to finish the job)
12X*14+(12X+12Y)T=16X*(12*2)
 SAVE TIME AND DIVIDE BY 12 
14X+(X+Y)T=32X
(X+Y)T=18X
T=18X/X+Y

Substitute X=2Y from Equation 1

T=36Y/3Y
T=12
12+14=26 Total Days

It takes 16 days for 48 women to complete a job that

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards