time and work

Question

james and ghansu can do a piece of work in 9 days by working together . their skills of doing work are in the ratio 3:5 in how many days will take to complete the work if he is engaged alone.

 

(a)24

(b)20

(c)15

(d)22

(e)23

Answer 1

You have not specified who is engaged alone, James or Ghansu.  Let's solve for both.

 

This is a distance = velocity x time problem.

 

D=distance, in this case it is measured in jobs done, i.e., 1.

 

D=1

 

VJG=velocity of J and G working together, measured as jobs per day.

 

VJ=velocity of J working alone, measured as jobs per day.

 

VG=velocity of J working alone, measured as jobs per day.

 

TJG=time to do the one job when both J and G work, measured in days.  This is given as 9

 

TJG=9

 

If days per job is 9, then jobs per day is 1/9.

 

VJG=1/9.

 

But VJG=VJ+VG and VJ/VG=3/5

 

So:

 

VJ=(3/5)VG

 

(3/5)VG+VG=1/9

 

(8/5)VG=1/9

 

VG=(5/8)*(1/9)=(5/72) jobs per day.

 

VJ+(5/72)=(1/9)

 

VJ=(1/9)-(5/72)=(8/72)-(5/72)=3/72 jobs per day.

 

days/job is the inverse of jobs per day.

 

It takes G 72/5 days to do the job alone.

 

It takes J 72/3 days to do the job alone.