Question

A takes 2 days to complete one-third of a
Job, B takes 2 days to complete one-sixth
of the same work and C takes 4 days to
complete half the job. If all of them work
together for 2 days and C quits, how long
will it take for A and B to complete the
remaining work done?
5 days
4 days
1 day
2 days​

Answer 1

Answer:

in 2 days is correct answer

Answer 2

Answer:

⇒ therefore the remaining work can be done by A and B in 1 day

Step-by-step explanation:

Given data

A takes 2 days to complete one - third of a job

B takes 2 days to complete one - sixth of the same job

C takes 4 days to complete half of the job

All of them worked together for 2 days after that C quits

The remaining work is completed by A and B together

here we need to find how many days will take A and B to complete the remaining job

Let x be the total work / job      

work can be done by A in 2 days = $\frac{x}{3}$    

⇒ work can be  done by A in 1 day = $\frac{\frac{x}{3} }{2}$ = $\frac{x}{6}$  

work can be  done by B in 2 days = $\frac{x}{6}$  

⇒ work can be done by B in 1 day = $\frac{\frac{x}{6} }{2}$ = $\frac{x}{12}$  

work can be done by C in 4 days = $\frac{x}{2}$  

⇒ work can be  done by C in 1 day = $\frac{\frac{x}{2} }{4}$  = $\frac{x}{8}$  

the work can be  done A, B and C in 1 day = $\frac{x}{6}+ \frac{x}{12} +\frac{x}{8}$  

                                                         = $\frac{4x+2x+3x}{24}$  = $\frac{9x}{24}$  = $\frac{3x}{8}$

⇒ the total work completed by A, B and C together 2 days =

           = 2(the work done by A, B and C in 1 day) =  $2(\frac{3x}{8})$ = $\frac{3x}{4}$  

the remaining work = $x - \frac{3x}{4}$ = $\frac{4x- 3x}{4}$ = $\frac{x}{4}$  

⇒ the work can be done by A and B together in 1 day

                  = $\frac{x}{6} + \frac{x}{12}$  =  $\frac{2x+ x}{12}$ =  $\frac{3x}{12}$  = $\frac{x}{4}$  which is same as remaining work

⇒ therefore the remaining work can be done by A and B in 1 day