Question

A and B together can do a work in 16 days, which B and C together can do in 32 days. After A has been working at it for 15 days and B for 13 days, C finished it in 10 days. In how many days A and C alone will do the work respectively?

Answer 1

Answer:

A=24days , B=48days , C=96days

A+C=96/5 days

Step-by-step explanation:

Let X,Y and Z be the work-fraction of 1 day's output of A,B and C.

X+Y = 1/16------[1]

and Y+Z = 1/32------[2]

Therefore on adding eq[1] nd [2],we get:-

X+2Y+Z = 3/32.

Given that:- 15x+13y+10z=1

15x+15y-2y+10z=1

15(x+y)-2(y+z)+12z=1

15/16-2/32+12z=1

28/32+12z=1

12z=4/32

z=1/96

Now,

y=1/32-1/96 = 2/96 = 1/48

x=1/16-1/48 = 2/48 = 1/24

A and c together can do the work in 1/24+1/96= 5/96

So time taken by A and C to finish jointly is 96/5days = 15.2 days