Question

two workers A and B together could finish a work in 8 days. they worked together for 6 days and A left the work. the remaining work was completed by B alone in 6 days. how many days would each take to complete the work individually

Answer 1

Solution:-

Let A takes 'x' time to complete the work alone.
So, one day work of A = 1/x
And,
Let B takes 'y' time to complete the work alone.
So, one day work of B = 1/y
One day work of both A and B when they work together = 1/8
Now, 
⇒ 1/x + 1/y = 1/8
They work together for 6 days and A left. That means 6/8 work had already been completed.
So, remaining work = 1 - 6/8
= 2/8 
= 1/4
So, 1/4th part of total work is still remaining and B finished this 1/4th part in 6 days.
⇒ 6(1/y) = 1/4
⇒ 6/y = 1/4
⇒ y = 24
Hence B will take 24 days to complete the work alone.
Now,
Substituting the value of y = 24, we can have the value of x.
1/x + 1/y = 1/8
⇒ 1/x + 1/24 = 1/8
⇒ 1/x = 1/8 - 1/24
⇒ 1/x = 2/24
⇒ 1/x = 1/12
⇒ x = 12 
So, A will take 12 days to complete the work alone.

Answer 2

Answer:

Step-by-step explanation:

Let A takes 'x' time to complete the work alone.

So, one day work of A = 1/x

Let B takes 'y' time to complete the work alone.

So, one day work of B = 1/y

One day work of both A and B when they work together = 1/8

Now, 

⇒ 1/x + 1/y = 1/8

They work together for 6 days and A left.

That means 6/8 work had already been completed.

So, remaining work = 1 - 6/8

= 2/8 

= 1/4

So, 1/4th part of total work is still remaining and B finished this 1/4th part in 6 days.

⇒ 6(1/y) = 1/4

⇒ 6/y = 1/4

⇒ y = 24

Hence B will take 24 days to complete the work alone.

Now,

Substituting the value of y = 24, we can have the value of x.

1/x + 1/y = 1/8

⇒ 1/x + 1/24 = 1/8

⇒ 1/x = 1/8 - 1/24

⇒ 1/x = 2/24

⇒ 1/x = 1/12

⇒ x = 12 

So, A will take 12 days to complete the work alone.