Question

A and b can do a given piece of work 8 days ; b and c can do the same work in 12 days and A B C complete it in 6 days in how many days can A and c finish it.




exaplain correctly ​

Answer 1

Consider the provided information.

A and B can do a given piece of work in 8 days.

The one day work of A and B is =

$\frac{1}{8}$

B and C can do the same work in 12 days

The one day work of B and C is =

$\frac{1}{12}$

Let A and C complete the work in x days

The one day work of A and C is =

$\frac{1}{x}$

A, B and C can do a given piece of work in 6 days.

The one day work of A, B and C is =

$\frac{1}{6}$

Thus, (A+B+B+C+C+A)’s one day’s work =

$= \frac{1}{8}+\frac{1}{12}+\frac{1}{x}$

2(A+B+C)=

$\frac{3x+2x+24}{24x}$

$2\times\frac{1}{6} =\frac{5x+24}{24x}$

8x=5x+248x=5x+24

$\begin{gathered}3x=24\\x=8\end{gathered}$

Answer 2

Answer:

One day work of A+B =1/8

One day work of B = 1/8 – A -------- (1)

One day work of B+C = 1/12

One day work of C = 1/12 – B -------- (2)

One day work of A+B+C = 1/6---------(3)

Then (2) in (3)

A+ B+ 1/12 -B = 1/6 ------------- A=1/12

Then (1) in (3)

A+ 1/8 -A + C = 1/6 ------------- C = 1/24

There fore A +C = 1/12 + 1/24

A+C = 3/24

= 1/8

So no of days to complete work in 8 days when A and C work together