If 12 men and 16 women can do a piece of work in 5 days and 13 men...

[AAPL]

GMAT Prep

If 12 men and 16 women can do a piece of work in 5 days and 13 men and 24 women can do it in 4 days, how long will 7 men and 10 women take to do it?

A. 4.2 days
B. 6.8 days
C. 8.3 days
D. 9.8 days
E. 10.2 days

OA C

[Jay@ManhattanReview]

GMAT Prep

If 12 men and 16 women can do a piece of work in 5 days and 13 men and 24 women can do it in 4 days, how long will 7 men and 10 women take to do it?

A. 4.2 days
B. 6.8 days
C. 8.3 days
D. 9.8 days
E. 10.2 days

OA C

Given that 12 men and 16 women can do a piece of work in 5 days, we have 12*5 = 60 men and 16*5 = 80 women can do a piece of work in 5/5 = 1 day;

Similarly,

Since 13 men and 24 women can do it in 4 days, 13*4 = 52 men and 24*4 = 96 women can do it in 4/4 = 1 day.

Thus, 60 men + 80 women = 52 men + 96 women => 1 man = 2 women

Thus, 7 men and 10 women = 7 men + 10/2 = 5 men = 12 men

So, the question is: how long will 12 men take to do the work?

From the information, we can say that 12 men + 16/2 = 8 men = 20 men can do a piece of work in 5 days; thus, 12 men can do the same work in (5*20)/12 = 25/3 = 8.33 days

The correct answer: C

Hope this helps!

-Jay
_________________
Manhattan Review Test Prep

Locations: Manhattan Review Bangalore | Chennai | GRE Prep Hyderabad | Himayatnagar GRE Coaching | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

[Scott@TargetTestPrep]

GMAT Prep

If 12 men and 16 women can do a piece of work in 5 days and 13 men and 24 women can do it in 4 days, how long will 7 men and 10 women take to do it?

A. 4.2 days
B. 6.8 days
C. 8.3 days
D. 9.8 days
E. 10.2 days

OA C

Solution:

We can let the time it takes 1 man to finish the work = m, and thus the rate of 1 man = 1/m. Likewise, we can let the time it takes 1 woman to finish the work = w, and thus the rate of 1 woman = 1/w.

Thus, the combined rate of 12 men and 16 women is 12/m + 16/w. Since they can finish the work in 5 days, their combined rate is also equal to 1/5. Thus, we have:

12/m + 16/w = 1/5

Multiplying both sides of the equation by 5mw, we have:

60w + 80m = mw

Similarly, the combined rate of 13 men and 24 women is 13/m + 24/w. Since they can finish the work in 4 days, their combined rate is equal to 1/4. Thus, we have:

13/m + 24/w = 1/4

Multiplying both sides of the equation by 4mw, we have:

52w + 96m = mw

So, we have 60w + 80m = 52w + 96m (since they both equal mw).

60w + 80m = 52w + 96m

8w = 16m

w = 2m

We can now substitute w = 2m into the first equation, 12/m + 16/w = 1/5, to solve for m:

12/m + 16/(2m) = 1/5

12/m + 8/m = 1/5

20/m = 1/5

m = 100

Since m = 100 days, w = 200 days. The rate of 1 man is 1/100 and the rate of 1 woman is 1/200. Thus, the rate of 7 men and 10 women is 7/100 + 10/200 = 7/100 + 5/100 = 12/100, and the time for them to finish the same work is 1/(12/100) = 100/12 = 8.3 days.

Alternate Solution:

Alternatively, we can interpret the equation w = 2m as follows:

The time required for 1 woman to finish the job is twice that of a man, or, in other words, the job done by 2 women is equivalent to the job done by 1 man. We know 12 men and 16 women finish the job in 5 days, and as per the above discussion, this is equivalent to the job done by 12 + 16/2 = 20 men.

The question is asking for the time required to finish the job with 7 men and 10 women working, which is equivalent to 7 + 10/2 = 12 men working. We can set up an inverse proportion to find the required time: If 20 men finish a job in 5 days, then 12 men finish the job in how many days? Letting this unknown quantity be x, we have

20*5 = 12*x

x = 100/12 = 8.3 days

Answer: C