Question

3 men and 4 women can finish a piece of work in 12 days whereas 5 men and 4 women can complete the same work in 9 days.find the ratio of the amount of work done by a man to the amount of work done by a woman.

Answer 1

3:2

This is the Correct answer

Answer 2

Answer:

find x:y

3X+5Y=12----(1)

3x=12-5y

x=(12-5y)/3----(3)

input equation 3 into equation 2

5x+4y=9-----(2)

but x=(12-5y)/3----(3)

therefore 5(12-5y)/3+4y=9

(60-25y)/3+4y=9

(60-13y)/3=9

multiply both sides by 3

60-25y+12y=27  

collect like terms

60-27=25y-12y

33=13y

y=33/13

solve for the value of x

5x+4y=9--(2)

y=33/13

5x+4(33/13)=9

5x+132/13=9

5x=9-132/13

5x=-15/13

x=-3/13 or 3/13  

to find the ratio of x to y

(33/13)/(-3/13)=-11

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