Three boys and four men can complete a job together in 8 days. If the

Question

Three boys and four men can complete a job together in 8 days. If the work rate of each woman is twice that of a boy and two-thirds that of a man, how many days will it take for six women to complete the same job?

A. 5 5/9 days
B. 6 days
C. 10 days
D. 12 days
E. 15 days

A. 5 5/9 days
B. 6 days
C. 10 days
D. 12 days
E. 15 days

gmatophobia · Answer

Units of work done by 1 boy =  b

Units of work done by 1 men =  m

Work done per day by 3 boys and 4 men =  3b + 4m  units

Work done by 3 boys and 4 men in 8 days = Total Work =  8*(3b + 4m) = 24b + 32m  units

Assume that each woman does  w  units of work each day.

"...work rate of each woman is twice that of a boy..."

w = 2b

b = \frac{w}{2}

"...two-thirds that of a man..."

w = \frac{2}{3}m

m = \frac{3}{2}w

We can use the values to find the total units of work in terms of  'w'

8*(3b + 4m) = 24b + 32m = 24*(\frac{w}{2}) + 32*(\frac{3}{2}w) = 60w

Work done by  6  women per day =  6w

Number of days =  \frac{60w}{6w} = 10

Option C

iipshitaaaa · Answer

Setting up the equation for men and boys :-

3/B+4/M=1/8

Given data about the rate of each women :- 
2/B=2/3M 
B=3M

Therefore,
3/3M+4/M=1/8
M=40

Rate of 6 women :- 
2/3M = (2/3*120)*6 = 1/10

Time = 10 days.

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sayan640 · Answer

Lets Say ,

1 boy in 1 day does x part
1 woman in 1 day does 2x part
1 man in 1 day does 3x part since (2x *3/2)

Let the total work =W and 6 women take ' d ' days to complete the entire work.
Hence,
work done by 3 boys and 4 men = work done by 6 women
w / ((3x +12x ) * 8 )= w / (12x *d)
d= 10

C is the answer.

piermacabj · Answer

According to the data you have the following relationship:

1W = 2/3 M = 2B

So you can transform the initial information (3B + 4M Finish a job in 8 days, 1/8 per day) in Women

1W = 2B 
1.5W = 3B

1W = 2/3M
6W = 4M

You end up with 7.5W = 3B + 4M; So you can equal it to 1/8 to know what One Woman can work in a day

7.5 W = 1/8 
W = 1/60 (of the job per day)

Now they are asking you for 6W:

6W = 6(1/60)
6W = 1/10 (of the job per day)

Which means they can finish the job in 10 day, Alternative C

ravi1522 · Answer

Hello ,
Lets assume rate of boy as 1 
as work rate of each woman is twice that of a boy and two-thirds that of a man
so Rate of woman will be 2
so rate of men will be 3
so total time taken to complete work by woman will be ( 3*1+4*3)*8/(6*2)

so we get answer as 10 days 
so answer will be choice C
Thanks

Gimmy · Answer

Rate of 1 boy = 1/b; rate of 1 man = 1/m
Rate of 3 boy = 3/b; rate of 4 men = 4/m
Rate of 1 woman = 2/b or 2/3m
3/b + 4/m = 1/8 (3 boys and 4 men take 8 days to complete)
3/b = rate of 1.5 women and 4/m = rate of 6 women
Rate of 7.5 women = 1/8
Rate of 6 women = 1/8 x 4/5 = 1/10 -> 10 days

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