Question

the work done by x-3 man In 2X+1 days and the work done by 2 X+1 men in X+4 days are in the ratio 3:10. find the value of x​

Answer 1

We have that the work is in the Ratio of 3:10 So if the 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