Question 10

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

Solution

$$1M+3W+4B$$ = $$\frac{1}{96}$$-------(1)

$$2M+8B=\frac{1}{80}$$-------(2)

$$2M+3W=\frac{1}{120}$$-------(3)

on solving (1) and (2)

(1)x2 - (2)Ā 

$$\rightarrow2M+6W+8B-2M-8B=\frac{2}{96}-\frac{1}{80}$$Ā 

$$\rightarrow6W=\frac{1}{120}$$Ā 

$$\rightarrow$$ $$W=\frac{1}{720}$$

on substitutingĀ $$W=\frac{1}{720}$$ 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 = $$\frac{480}{11}=43\frac{7}{11}$$Ā hours.

so the answer is option C.


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