Question

The work done by (x 3) men in (2x +1) days and the work done by ( 2x + 1) men in (x + 4) days are in the ratio 3 : 10. Find the value of x.

Answer 1

Answer:  x=6  or x=-1/2

Step-by-step explanation:  We have that the work is in the Ratio of 3:10 total work was 13W; then :

3W was done by x-3 men in 2x+1 days ;  10W was done by 2x+1 men in x+4 days

Work done per day by x-3 men=3W/(2x+1)  

Work done per day by 1 man=3W/( (2x+1) * (x-3) )  

Work done per day by 2x+1 men=10W/(x+4)  

Work done per day by 1 man=10W/( (x+4) *(2x+1)  )

Now assuming that the  work capacity per man would not change due to the number of men:

     3W/( (2x+1) * (x-3) ) =10W/( (x+4) *(2x+1)  )

 3* (x+4) *(2x+1) = 10 * (2x+1) * (x-3)

  x=-1/2  or ...

  3x + 12 = 10x - 30

  7x = 42

 x=6

Answer : x=-1/2   or  x=6