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LiRa [457]
2 years ago
11

Two men and 7 women can together do a piece of work in 4 days. It is done by 4 men and 4 women in 3 days. How long would it take

for one man or one woman to do the work
Mathematics
1 answer:
liraira [26]2 years ago
7 0

Answer:

12 days

Step-by-step explanation:

Time taken by one man = x days , and that by 1 boy = y days


work done in 1 day by one man = 1/x


work done in 1 day by one boy= 1/y


work done by 2 men in one day = 2/x


work done by 7 boys in one day = 7/y


2/x + 7/y = 1/4      -----> [ 1]


work done by 4 men in one day = 4/x

work done by 4 boys in one day = 4/y


4/x + 4/y = 1/3       ----> [2]


Multiplying  equation 1 by  , 2 ,  


2(2/x + 7/y = 1/4   )

 = 4/x + 14/y = 1/2           ---> [3]


solving equations 2 and 3




 4/x + 4/y = 1/3  

- 4/x + 14/y = 1/2  

==============

-10/y = 2-3/6

-10/y = -1/6


-1/6y = -10

y = -10 × 6/-1

  = 60 


2/x + 7/y = 1/4

2/x + 7/60 = 1/4

7/60 - 1/4 = -2/x

-8/60 = -2/x


-120 = -8x

x = -120/-8

x = 15


=================================


Time taken by 1 man to do the  whole job = 15 days

time taken by 1 boy to do the whole  job = 60 days


time taken by one boy and one man to do one day's work = 1/60 + 1/15

                                         = 1/60 + 4/60

                                         = 5/60  = 1/12

Together they can do it in 12 days !





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