One man, 3 women and 4 boys can do a piece of work in 96 hours, 2 men and 8 boys can do it in 80 hours, 2 men and 3 women can do it in 120 hours. 5 men and 12 boys can do it in
$$1M+3W+4B$$ = $$\frac{1}{96}$$-------(1)
$$2M+8B=\frac{1}{80}$$-------(2)
$$2M+3W=\frac{1}{120}$$-------(3)
on solving (1) and (2)
(1)x2 - (2)
$$\rightarrow2M+6W+8B-2M-8B=\frac{2}{96}-\frac{1}{80}$$
$$\rightarrow6W=\frac{1}{120}$$
$$\rightarrow$$ $$W=\frac{1}{720}$$
on substituting $$W=\frac{1}{720}$$ in (3) we will get $$M=\frac{1}{480}$$
on substituting both in (1), we will get $$B=\frac{1}{960}$$
now, $$5M+12B=\frac{5}{480}+\frac{12}{960}=\frac{22}{960}=\frac{11}{480}$$
so no.of hours = $$\frac{480}{11}=43\frac{7}{11}$$ hours.
so the answer is option C.
Create a FREE account and get: