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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

A

`39 1/11` घंटे

B

`42 7/11` घंटे

C

`43 7/11` घंटे

D

44 घंटे

Text Solution

Verified by Experts

The correct Answer is:
C
`M+3W+4B=1/96`.........(i)
`2M+8B=1/80` ........(ii)
`2M+3W=1/120` .........(iii)
समी. (i) `Xx2 -` समी. (ii) करने पर
`2M + 6W+ 8B- 2M - 8B =1/48 -1/80`
`implies 6W=(5-3)/240=1/120`
`impliesW=1/720`
w→ एक महिला की कार्य क्षमता
M → एक पुरुष की कार्य क्षमता
B→ एक लड़के की कार्य क्षमता
`2M+3W = 1/120`
`2M+3xx1/720=1/120`
`implies 2M=1/120 - 1/240 =(2-1)/240 =1/240`
`implies M=1/480`
`:. 2M+8B=1/80`
`implies 2xx1/480+8B=1/80`
`implies 8B =1/80 -1/240 =(3-1)/240 =1/120`
`:. B=1/960`
`:. 5M+12B=5xx 1/480+12xx 1/960`
`=1/96+1/80 =(5+6)/480 =11/480`
`:. 5` पुरुषों तथा 12 लड़के को कार्य संपन्न करने में लगा समय `=480/11 =43 7/11 hrs`
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