Mathematics

Question

8 men and 12 women can complete a certain job in 6 days,  the men work as 1.2 the rate at which the women worked.  How many men will be required to complete the job in 4 days 

Answer 1

men work 1.2 times the rate of women

8 men and 12 women is the same as 8 men and 10 men (instead of 12 women-10*1.2=12)

18 men do the job in 6 days

how many men does it take to do the job in 4 days ?

6/4=1.5

1.5*18=27 men to do the job in 4 days

 

also, this is an inverse proportion or inverse variation; y=k/x

18 men in 6 days, how many men in 4 days ?

18=k/6

k=18*6

k=108

y=108/4

y=27 men

 

 

Answer 2

Let the women's rate of work be the standard

 

The size of the job can be measured in woman.days

 

Job size = (8*1.2*6) + (12 *6) = 129.6 woman.days

 

Let X be the number of men required to complete the same job in 4 days

 

then, (1.2*X)*4 = 129.6; therefore X = 129.6/4.8 = 27

 

Hence 27 men would be required to complete the same job in 4 days