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 then 5 men and and 12 boys can do it in
Answers
Answer:
Step-by-step explanation:
Let the Man be "m" , Boys be "B" and Women be "w".
A.T.Q.
Condition |,
1 Man + 3 Women + 4 Boys can do the work in 96 hours.
=> 1M + 3W + 4B = 96 Hours.
In One Hour work done is
=> 1 M + 3W + 4B = 1/96 hrs.
_______(1)
Condition ||,
2 Man + 8 Boys complete the work in 80 hours.
=> 2M + 8B = 80 hrs.
In One Hour the work done is
=> 2M + 8B = 1/80_______________(2)
Condition |||,
2 Man + 3 Women can do the work in 120 hours.
=> 2M + 3W = 120
In One Hour Work done is
=> 2M + 3W = 1/120___________(3)
In EQ (1) & (2). By Elimination Method,
Multiplying EQ (1) by 2.
=> 2( 1M + 3W + 4B) = 2/96
=> 2M + 6W + 8B = 1/48
Now,
2M + 6W + 8B = 1/48
2M + 8B = 1/80
_______________________
6W = 1/48 - 1/80
=> 6W = ( 5-3)/240
=> 6W = 2/240
=> 6W = 1/120
=> W = 1/720.
Putting (W = 1/720) in EQ (3).
2M + 3/720 = 1/120
=> 2M = 1/120 - 1/240
=> 2M =( 2-1)/240
=> M = 1/240×2
=> M = 1/480.
Putting the values of W & Min EQ (1).
=> 1/480 + 3/720 + 4B = 1/96
=> 4B = 1/96 - 1/480 - 1/240
=> 4B = ( 5 - 1 - 2)/480
=> 4B = 2/480
=> B = 1/240×4
=> B = 1/960
Now,
5M + 12B = ? Hours.
In One Hour,
M = 1/480 & B = 1/960.
Hence,
5 Man & 12 Boy can complete the work
=> 5/480 + 12/960
=> 1/96 + 1/80
=> ( 5+6)/ 480
=> 11/480
Hence,
5Man & 12Boys can do it in 480/11 Hours.