Question

A, b and c can do a piece of work individually in 8, 12 and 15 days, respectively. a and b start working but a quits after working for 2 days. after this, c joins b till the completion of work. in how many days will the work be completed?

Answer 1

a can do a piece of work = 8 days
b can do a piece of work = 12 days
c can do a piece of work = 15 days

a and b start working together ,
together they can do work = 8 × 12/(8 + 12) days = 24/5 days
means together a and b can do 5/24th of work in 1 day .
∴ 5/12th part of work completed in 2days .
now, after two days a quits .
Rest part of work is done by b and c together.
∴ rest part of work = 1 - 5/12 = 7/12th part of work.

But we observed , b and c can do work = 12 × 15/(12 + 15) days = 20/3 days
So, number of days to complete 7/12th part of work = 7/12 × 20/3 = 140/36 days

Hence, b and c together complete the 7/12th part of work = 35/9 days = 3 8/9 days .

Answer 2

Hello Dear.

Here is your answer---

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A's can do a Piece of Work in 8 Days.
A's one Day Work = 1/8 Days

B's can do a Piece of Work in 12 Days.
B's one day work = 1/12 Days. 

C's can do a Piece of Work in 15 Days.
C's one day Work = 1/15 Days.

As per as Question, A and B starts the Works Together,

Thus,  Time taken by Both to complete the Works =
         A's one day work + B's one day work
     = 1/8 + 1/12
     = (3 + 2)/24         [Taking L.C.M.]
     = 5/24

∴ Time taken by A and B to complete the work together = 24/5 Days.

In one Day, the work done by A and B is 5/24 th part of the work.
In 2 Days-------------------------------------------(5/24) × 2 th part of work
                                                                  = 5/12th Part of the Work.

Thus, Part of the Work that is Remaining = 1 - 5/12
                                                                  = (12 - 5)/12
                                                                  = 7/12
After 2 Days, C joins the work..

Thus, work done by B and C in one Day = 1/B + 1/C
                                                                 = 1/12 + 1/15
                                                                 = (4 + 5)/60 
                                                                 = 9/60
                                                                 = 3/20 
Thus, Remaining work(7/12th part) will be completed by B and C
       =  $\frac{7/12}{3/20}$
       = 140/36
       = 70/18
       = 35/9 Days.

Hence, The Total Work will be Done in (2 Days + 35/9 Days)
                                                            = (18 + 35)/9 Days.
                                                            = 53/9 Days.
                                                            = $5 \frac{8}{9}$ Days.

Thus, the Total time taken will be $5 \frac{8}{9}$ Days.


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I Anticipate it will helps u. 

Have a Marvelous Days.