Question

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

Answer 1

Solutions :-

Given :
A and B can do a piece of work in 8 days.
B and C can do the same work in 12 days.
And A, B and C can complete it in 6 days.


(A + B)'s one day work = 1/8
(B + C)'s one day work = 1/12
(A + B + C)'s one day work = 1/6


Find the (A + C)'s one day work :-

[(A + B + C) - (B + C)] + [(A + B + C) - (A + B)]
= (1/6 - 1/12) + (1/6 - 1/8)
= (2 - 1)/12 + (4 - 3)/24
= 1/12 + 1/24
= (2 + 1)/24
= 3/24
= 1/8


Hence,
A and C finish it in 8 days.

Answer 2

If A and B can do that task in 8 day

Then they will do 1/8 part of it in one day

B and C can do that task in 12 days

So they do 1/12th part of work in one day

So, (A+B) + (B+C) can do 1/8 + 1/12 = 5/24 part of work ————(1)

And, we know that 1/6th part of work is done by A+ B + C in one day------(2)

Solving,Both equation

A+2B+C = 5/24——(1)

A+B+C =1/6——(2)

Multiplying equation (2) by number 2 and subtracting from (1) to eliminate B

We get,

A+C = 3/24

A+C = 1/8

Hence A and C can do 1/8th part of task in one day

So, They will require a total of 8 days to complete the task when they both (A and C) will work together.

Hope you understood

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