A group of men and women decide to finish a task in 20 days

Question

A group of men and women decide to finish a task in 20 days. 10 men can also finish the same task in 20 days. 6 men start working and on the 7th day, 2 women join. On the 8th day, 2 more women join and so on. After working for 15 days from the beginning, it is found that only 60% of the work is completed. On the 16th day, x more women join and worked till the end. If the task was finished on time, what is the value of x?

A. 12
B. 18
C. 24
D. 30
E. 36

Source : Wizako

A. 12
B. 18
C. 24
D. 30
E. 36

Source : Wizako

Kinshook · Accepted Answer

Given: A group of men and women decide to finish a task in 20 days. 10 men can also finish the same task in 20 days. 6 men start working and on the 7th day, 2 women join. On the 8th day, 2 more women join and so on.

Asked: After working for 15 days from the beginning, it is found that only 60% of the work is completed. On the 16th day, x more women join and worked till the end. If the task was finished on time, what is the value of x?

Task = 200 man-days
15*6 man-days + (2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18) women days = 60%*200 = 120 man-days
90 man-days + 90 women-days = 120 man-days
1 man-day = 3 women-days

Days left
Women = 18 + x
Men = 6 
Work left = 200 -120 = 80 man-days
Days left = 20 - 15 = 5 days
6*5 + (18+x)*5*1/3 = 80
(18+x)5/3 = 50
18+x = 30
x = 12

IMO A

Dev23 · Answer

10 men complete a work in 20 days 
Therefore 1 man's 1 day work = 1/200=1/2%

6 Men working for15 Days complete = 6*15*1/2=45%

Let g be % of work done by 1 girl in 1 day
so 45 + ( 2g+4g+ 6g........18g)= 60
90g=15
so g=1/6

Now it is given that work needs to be completed in 20 days
Days left to complete the work = 20-15=5 
work left = 40%

So 6*5*1/2 + 18*5*1/6 +x*5*1/6 = 40
15 + 15 + 5/6x = 40
5/6x = 10
x= 12

GmatPoint · Answer

Let each man do 1 unit of work per day.

Since 10 men can finish the job in 20 days, total work = 20*10 = 200 units

On 15th day, total work finished = 60*200/100 = 120 units.

6 men for 15 days will complete 15*6 = 90 units.

Thus, work done by women = 120 - 90 = 30 units.

Let 1 woman do y units of work per day.

Thus, work done by women = 2*9*y + 2*8*y+......2*y = (2*9/2)(y + 9y) = 90y

Thus, 90y = 30, y = 1/3

Now, a total of 18 women are working already, and x more have joined.

Total days left = 5

Thus, the Total work that will be done by 6 men = 5*6 = 30 units.

Work left = 200 - 120 - 30 = 50 units.

So, Work left for women = 50 units.

5*(18+x)*1/3 = 50 units

18+x = 30 units

x = 12 units.

Thus, the correct option is A.

ThatDudeKnows · Answer

Let's make the task solving GMAT problems, and let's say each man can solve one GMAT problem per day.

10 men can finish the task in 20 days, so the task is solving 200 GMAT problems.

Let's look at days 1 through 15.
We are told that 60% of the work is completed in that timeframe, so 120 questions
6 men work each day, so they solve 90 GMAT problems. Women solved 30 GMAT problems. How many days do women work?
Day 7: 2
Day 8: 4
9:6
10: 8
11: 10
12: 12
13: 14
14: 16
15: 18
That's a total of 90 days worked and they solve 30 questions, so each woman solves 1/3 of a question per day. 
We now have rates of 1 question per day for men and 1/3 of a question per day for women.

Okay, so now let's look at days 16 through 20.
That's five days and we have 80 questions to solve. 
The 6 men will solve 30, so the women need to solve 50. 
50 questions in 5 days is 10 per day, so we need a total of 30 women. We already have 18, so we need to add 12 starting day 16.

Answer choice A.

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A group of men and women decide to finish a task in 20 days

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