NandishSS wrote: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
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 also 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.
Answer:
C
